diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2215278562..5af634a9f0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -19,7 +19,7 @@ For a list of breaking changes, check [here](#breaking-changes).
 
 ## Unreleased
 
-- ...
+- [#2159](https://github.com/clj-kondo/clj-kondo/issues/2159): New linter, `:invalid-fn-name`
 
 ## 2023.12.15
 
diff --git a/doc/linters.md b/doc/linters.md
index c1a56a7269..2a750b9bed 100644
--- a/doc/linters.md
+++ b/doc/linters.md
@@ -47,6 +47,7 @@ configuration. For general configurations options, go [here](config.md).
     - [Format](#format)
     - [Def + fn instead of defn](#def--fn-instead-of-defn)
     - [Inline def](#inline-def)
+    - [Invalid fn name](#invalid-fn-name)
     - [Invalid arity](#invalid-arity)
     - [Conflicting arity](#conflicting-arity)
     - [Reduce without initial value](#reduce-without-initial-value)
@@ -845,6 +846,21 @@ See [issue](https://github.com/clj-kondo/clj-kondo/issues/1920).
 
 *Example message:* `inline def`.
 
+### Invalid fn name
+
+**Keyword:** `:invalid-fn-name`.
+
+*Description:* warn when a function's name is not valid. If present, it should
+be an unquoted symbol.
+
+*Default level:* `:error`.
+
+*Example trigger:* `(fn :fn-name [x] (inc x))`.
+
+*Example message:* `First arg of fn should be a symbol, params vector or arity clause`.
+
+*Config:*
+
 ### Invalid arity
 
 **Keyword:** `:invalid-arity`.
diff --git a/src/clj_kondo/impl/analyzer.clj b/src/clj_kondo/impl/analyzer.clj
index 81b28db340..470aa2e22b 100644
--- a/src/clj_kondo/impl/analyzer.clj
+++ b/src/clj_kondo/impl/analyzer.clj
@@ -934,6 +934,21 @@
 (defn- let? [x]
   (one-of x [[clojure.core let] [cljs.core let]]))
 
+(defn- invalid-fn-name? [?name-expr]
+  (let [valid? (some-fn utils/list-node? ; fn body (usually 1 of many)
+                        utils/vector-node? ; fn args
+                        utils/symbol-token?)] ; fn name
+    (not (valid? ?name-expr))))
+
+(defn- reg-invalid-fn-name! [ctx expr filename]
+  (findings/reg-finding!
+   ctx
+   (node->line
+    filename
+    expr
+    :invalid-fn-name
+    "First arg of fn should be a symbol, params vector or arity clause")))
+
 (defn- def-fn? [{:keys [callstack]}]
   (let [[_ parent extra-parent] callstack]
     (or (def? parent)
@@ -985,6 +1000,10 @@
     (when (and (not (linter-disabled? ctx :def-fn))
                (def-fn? ctx))
       (reg-def-fn! ctx expr filename))
+    (when (and (not (linter-disabled? ctx :valid-fn-name))
+               ?name-expr
+               (invalid-fn-name? ?name-expr))
+      (reg-invalid-fn-name! ctx expr filename))
     (with-meta parsed-bodies
       (when arities
         (cond-> {:arity {:fixed-arities fixed-arities
diff --git a/src/clj_kondo/impl/config.clj b/src/clj_kondo/impl/config.clj
index b4b59f6f79..ada0ded989 100644
--- a/src/clj_kondo/impl/config.clj
+++ b/src/clj_kondo/impl/config.clj
@@ -26,6 +26,7 @@
               :private-call {:level :error}
               :inline-def {:level :warning}
               :def-fn {:level :off}
+              :invalid-fn-name {:level :error}
               :redundant-do {:level :warning}
               :redundant-let {:level :warning}
               :cond-else {:level :warning}
diff --git a/src/clj_kondo/impl/utils.clj b/src/clj_kondo/impl/utils.clj
index e320891297..5a9656831f 100644
--- a/src/clj_kondo/impl/utils.clj
+++ b/src/clj_kondo/impl/utils.clj
@@ -38,6 +38,10 @@
   (and (instance? clj_kondo.impl.rewrite_clj.node.seq.SeqNode n)
        (identical? :set (tag n))))
 
+(defn vector-node? [n]
+  (and (instance? clj_kondo.impl.rewrite_clj.node.seq.SeqNode n)
+       (identical? :vector (tag n))))
+
 ;;; end export
 
 (defn print-err! [& strs]
diff --git a/test/clj_kondo/main_test.clj b/test/clj_kondo/main_test.clj
index 9701baf938..7d8f61e940 100644
--- a/test/clj_kondo/main_test.clj
+++ b/test/clj_kondo/main_test.clj
@@ -60,6 +60,18 @@
       (is (empty? (lint! "(def x (reify Object (toString [_] \"x\")))" "--lang" (name lang) "--config" (pr-str config))))
       (is (empty? (lint! "(require '[some.ns :refer [my-reify]]) (def x (my-reify Object (toString [_] \"x\")))" "--lang" (name lang) "--config" (pr-str config)))))))
 
+(deftest invalid-fn-name-test
+  (assert-submaps
+   '({:row 1, :col 1, :level :error, :message "First arg of fn should be a symbol, params vector or arity clause"})
+   (lint! "(fn \"fn-name\" [x] (inc x))"))
+  (assert-submaps
+   '({:row 1, :col 6, :level :error, :message "First arg of fn should be a symbol, params vector or arity clause"})
+   (lint! "(map (fn 'symbol ([x] (inc x))) coll)"))
+  (assert-submaps
+   '({:row 1, :col 7, :level :error, :message "First arg of fn should be a symbol, params vector or arity clause"})
+   (lint! "(-> 7 (fn [x] (inc x)))"))
+  (is (empty? (lint! "(fn fn-name [x] (inc x))"))))
+
 (deftest redundant-let-test
   (let [linted (lint! (io/file "corpus" "redundant_let.clj"))
         row-col-files (map #(select-keys % [:row :col :file])