diff --git a/changelog/new_merge_pull_request_1378_from.md b/changelog/new_merge_pull_request_1378_from.md
new file mode 100644
index 0000000000..108d37bf8f
--- /dev/null
+++ b/changelog/new_merge_pull_request_1378_from.md
@@ -0,0 +1 @@
+* [#1378](https://github.com/rubocop/rubocop-rails/pull/1378): Add new `Rails/IndexNames` cop. ([@corsonknowles][])
diff --git a/config/default.yml b/config/default.yml
index 0e7d183460..1e7a530c6a 100644
--- a/config/default.yml
+++ b/config/default.yml
@@ -624,6 +624,16 @@ Rails/IndexBy:
   VersionAdded: '2.5'
   VersionChanged: '2.8'
 
+Rails/IndexNames:
+  Description: 'Checks for and removes custom index names. Since 7.1, Rails can ensure unique index names without exceeding the length limit.'
+  Enabled: pending
+  SafeAutoCorrect: false
+  StartAfterMigrationVersion: null
+  VersionAdded: <<next>>
+  VersionChanged: <<next>>
+  Include:
+    - db/**/*.rb
+
 Rails/IndexWith:
   Description: 'Prefer `index_with` over `each_with_object`, `to_h`, or `map`.'
   Enabled: true
diff --git a/lib/rubocop/cop/mixin/migrations_helper.rb b/lib/rubocop/cop/mixin/migrations_helper.rb
index 76dedda41f..4b5add9271 100644
--- a/lib/rubocop/cop/mixin/migrations_helper.rb
+++ b/lib/rubocop/cop/mixin/migrations_helper.rb
@@ -12,7 +12,7 @@ module MigrationsHelper
           (send
             (const (const {nil? cbase} :ActiveRecord) :Migration)
             :[]
-            (float _))
+            (float $_))
           _)
       PATTERN
 
@@ -21,6 +21,14 @@ def in_migration?(node)
           migration_class?(class_node)
         end
       end
+
+      def in_supported_migration?(node, minimum_version)
+        node.each_ancestor(:class).any? do |class_node|
+          migration_class?(class_node) do |version|
+            version >= minimum_version
+          end
+        end
+      end
     end
   end
 end
diff --git a/lib/rubocop/cop/rails/index_names.rb b/lib/rubocop/cop/rails/index_names.rb
new file mode 100644
index 0000000000..0a40b66cb1
--- /dev/null
+++ b/lib/rubocop/cop/rails/index_names.rb
@@ -0,0 +1,148 @@
+# typed: false
+# frozen_string_literal: true
+
+module RuboCop
+  module Cop
+    module Rails
+      # Checks for custom index names in migrations.
+      #
+      # @safety
+      #   Migration files must not be altered after they are run, and it is important to
+      #   run identical migrations in each environment. Autocorrect should only be used
+      #   while composing a migration, before executing it.
+      #   See: https://guides.rubyonrails.org/active_record_migrations.html#changing-existing-migrations
+      #
+      # @example
+      #   # bad
+      #   class ExampleMigration < ActiveRecord::Migration[7.2]
+      #     def change
+      #       change_table :users do |t|
+      #         t.index [:email], name: 'index_custom_name'
+      #       end
+      #     end
+      #   end
+      #
+      #   # bad
+      #   class ExampleMigration < ActiveRecord::Migration[7.2]
+      #     def change
+      #       add_index :table, :column, name: 'index_custom_name'
+      #     end
+      #   end
+      #
+      #   # good
+      #   class ExampleMigration < ActiveRecord::Migration[7.2]
+      #     def change
+      #       create_table :users do |t|
+      #         t.index [:email]
+      #       end
+      #     end
+      #   end
+      #
+      #   # ok (custom name may differentiate this index from an index on the same columns with default order)
+      #   class ExampleMigration < ActiveRecord::Migration[7.2]
+      #     def change
+      #       create_table :robots do |t|
+      #         t.index [:priority, :created_at],
+      #           name: 'index_robots_by_recency',
+      #           order: { priority: "ASC NULLS LAST", created_at: :asc }
+      #       end
+      #     end
+      #   end
+      #
+      #   # ok (custom name may be necessary to meet DB character limit for index names in older Rails versions)
+      #   class ExampleMigration < ActiveRecord::Migration[7.0]
+      #     def change
+      #       create_table :users do |t|
+      #         t.index [:email], name: 'index_custom_name'
+      #       end
+      #     end
+      #   end
+      #
+      class IndexNames < Base
+        include MigrationsHelper
+        include RangeHelp
+        extend AutoCorrector
+        extend TargetRailsVersion
+
+        minimum_target_rails_version 7.1
+
+        MSG = 'Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.'
+        RESTRICT_ON_SEND = %i[index add_index].freeze
+        # Keys that do not justify a duplicative index or a custom name, as they represent stricter column conditions.:
+        # unique, length, nulls_not_distinct
+        # Refer to: https://github.com/rails/rails/blob/b943622bdc746370ac860bfd3240cc0b8ca59d90/activerecord/lib/active_record/connection_adapters/abstract/schema_statements.rb#L1477
+        VALID_REASONS_FOR_CUSTOM_NAME = Set.new(%i[where type using comment algorithm include opclass order]).freeze
+
+        def on_send(node)
+          return unless node.last_argument&.hash_type?
+          return unless in_supported_migration?(node, 7.1)
+          return unless (name_pair = find_name_pair(node))
+
+          return if node.last_argument.pairs.any? { |pair| VALID_REASONS_FOR_CUSTOM_NAME.include?(pair.key.value) }
+
+          add_offense(node) do |corrector|
+            remove_name_argument(corrector, name_pair, node)
+          end
+        end
+
+        private
+
+        def find_name_pair(node)
+          node.last_argument.pairs.find { |pair| pair.key.value == :name || pair.key.value == 'name' }
+        end
+
+        def remove_name_argument(corrector, name_pair, node)
+          range = name_argument_range(name_pair, node)
+          corrector.remove(range)
+          remove_extra_comma_and_space(corrector, range, node)
+        end
+
+        def name_argument_range(name_pair, node)
+          hash_node = name_pair.parent
+          if hash_node.pairs.size == 1
+            # If name: is the only argument, remove the entire hash
+            range_between(node.arguments[-2].source_range.end_pos, node.source_range.end_pos)
+          else
+            # Remove the name: argument and any preceding comma and space
+            start_pos = previous_comma_pos(name_pair) || name_pair.source_range.begin_pos
+            range_between(start_pos, name_pair.source_range.end_pos)
+          end
+        end
+
+        def previous_comma_pos(pair)
+          source = pair.parent.source
+          pair_start = pair.source_range.begin_pos - pair.parent.source_range.begin_pos
+          previous_content = source[0...pair_start]
+          comma_index = previous_content.rindex(',')
+          comma_index ? pair.parent.source_range.begin_pos + comma_index : nil
+        end
+
+        def remove_extra_comma_and_space(corrector, removed_range, node)
+          remaining_source = remaining_source(node, removed_range)
+          next_relevant_content = remaining_source.lstrip
+          range_to_remove = if next_relevant_content.start_with?(',')
+                              space_after_comma(removed_range, next_relevant_content)
+                            else
+                              leading_space(remaining_source, removed_range)
+                            end
+
+          corrector.remove(range_to_remove)
+        end
+
+        def remaining_source(node, removed_range)
+          node.source[removed_range.end_pos - node.source_range.begin_pos..]
+        end
+
+        def space_after_comma(removed_range, next_relevant_content)
+          space_after_comma = next_relevant_content[1..].match(/\A\s*/)[0]
+          range_between(removed_range.end_pos, removed_range.end_pos + 1 + space_after_comma.length)
+        end
+
+        def leading_space(remaining_source, removed_range)
+          leading_space = remaining_source.match(/\A\s*/)[0]
+          range_between(removed_range.end_pos, removed_range.end_pos + leading_space.length)
+        end
+      end
+    end
+  end
+end
diff --git a/lib/rubocop/cop/rails_cops.rb b/lib/rubocop/cop/rails_cops.rb
index b7eddc4fe4..a6543e0e3d 100644
--- a/lib/rubocop/cop/rails_cops.rb
+++ b/lib/rubocop/cop/rails_cops.rb
@@ -69,6 +69,7 @@
 require_relative 'rails/ignored_columns_assignment'
 require_relative 'rails/ignored_skip_action_filter_option'
 require_relative 'rails/index_by'
+require_relative 'rails/index_names'
 require_relative 'rails/index_with'
 require_relative 'rails/inquiry'
 require_relative 'rails/inverse_of'
diff --git a/spec/rubocop/cop/rails/index_names_spec.rb b/spec/rubocop/cop/rails/index_names_spec.rb
new file mode 100644
index 0000000000..bb92503091
--- /dev/null
+++ b/spec/rubocop/cop/rails/index_names_spec.rb
@@ -0,0 +1,291 @@
+# frozen_string_literal: true
+
+RSpec.describe RuboCop::Cop::Rails::IndexNames, :config do
+  context 'Rails 7.0', :rails70 do
+    context 'when t.index has a custom name argument' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.0]
+            def change
+              change_table :users do |t|
+                t.index [:email], name: 'index_custom_name'
+              end
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when add_index has a name argument' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.0]
+            def change
+              add_index :table, :column, name: 'index_custom_name'
+            end
+          end
+        RUBY
+      end
+    end
+  end
+
+  context 'Rails 7.2', :rails72 do
+    context 'when using an earlier migration version' do
+      context 'when t.index has a custom name argument' do
+        it 'does not register an offense' do
+          expect_no_offenses(<<~RUBY)
+            class ExampleMigration < ActiveRecord::Migration[7.0]
+              def change
+                change_table :users do |t|
+                  t.index [:email], name: 'index_custom_name'
+                end
+              end
+            end
+          RUBY
+        end
+      end
+
+      context 'when add_index has a name argument' do
+        it 'does not register an offense' do
+          expect_no_offenses(<<~RUBY)
+            class ExampleMigration < ActiveRecord::Migration[7.0]
+              def change
+                add_index :table, :column, name: 'index_custom_name'
+              end
+            end
+          RUBY
+        end
+      end
+    end
+
+    context 'when t.index has a custom name argument' do
+      it 'registers an offense' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              change_table :users do |t|
+                t.index [:email], name: 'index_custom_name'
+                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+              end
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when t.index has no name argument' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email]
+              end
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when add_index has no name argument' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              add_index :table, :column
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when add_index is outside of a migration' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          def change
+            add_index :table, :column, name: 'index_custom_name'
+          end
+        RUBY
+      end
+    end
+
+    context 'when t.index is outside of a migration' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          def change
+            create_table :users do |t|
+              t.index [:email], name: 'index_custom_name'
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when unrelated index method has a name argument' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          index :email, name: 'index_custom_name'
+        RUBY
+      end
+    end
+
+    context 'when t.index has a custom name old style hash argument' do
+      it 'registers an offense' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], 'name' => 'index_custom_name'
+                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+              end
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when t.index has multiple arguments and custom name' do
+      it 'registers an offense' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], unique: true, name: 'index_custom_name'
+                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+              end
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when t.index has a reason for a custom name and possibly distinct index on the same keys' do
+      it 'does not register an offense' do
+        expect_no_offenses(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], include: :tags, name: 'index_custom_name'
+              end
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when correcting an offense' do
+      it 'removes the custom name argument without removing following arguments' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], name: 'index_custom_name', unique: true
+                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+              end
+            end
+          end
+        RUBY
+
+        expect_correction(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], unique: true
+              end
+            end
+          end
+        RUBY
+      end
+
+      it 'removes only the name argument when there are other arguments and starts at name:' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], unique: true, name: 'index_custom_name'
+                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+              end
+            end
+          end
+        RUBY
+
+        expect_correction(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], unique: true
+              end
+            end
+          end
+        RUBY
+      end
+
+      it 'removes the name argument when it is the only keyword argument' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], name: 'index_custom_name'
+                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+              end
+            end
+          end
+        RUBY
+
+        expect_correction(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email]
+              end
+            end
+          end
+        RUBY
+      end
+
+      it 'removes only the name => argument for classic hash style' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email], "name" => 'index_custom_name'
+                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+              end
+            end
+          end
+        RUBY
+
+        expect_correction(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              create_table :users do |t|
+                t.index [:email]
+              end
+            end
+          end
+        RUBY
+      end
+    end
+
+    context 'when add_index has a name argument' do
+      it 'registers an offense' do
+        expect_offense(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              add_index :table, :column, name: 'index_custom_name'
+              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid specifying a custom name for common indexes. Let Rails handle the index name automatically.
+            end
+          end
+        RUBY
+
+        expect_correction(<<~RUBY)
+          class ExampleMigration < ActiveRecord::Migration[7.2]
+            def change
+              add_index :table, :column
+            end
+          end
+        RUBY
+      end
+    end
+  end
+end