diff --git a/packages/babel-traverse/src/scope/lib/renamer.js b/packages/babel-traverse/src/scope/lib/renamer.js
index 317dea76aa..cdfd908196 100644
--- a/packages/babel-traverse/src/scope/lib/renamer.js
+++ b/packages/babel-traverse/src/scope/lib/renamer.js
@@ -108,7 +108,7 @@ export default class Renamer {
         path.isClassExpression(),
     );
     if (parentDeclar) {
-      const bindingIds = parentDeclar.getBindingIdentifiers();
+      const bindingIds = parentDeclar.getOuterBindingIdentifiers();
       if (bindingIds[oldName] === binding.identifier) {
         // When we are renaming an exported identifier, we need to ensure that
         // the exported binding keeps the old name.
diff --git a/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/input.mjs b/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/input.mjs
new file mode 100644
index 0000000000..cee2ccf058
--- /dev/null
+++ b/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/input.mjs
@@ -0,0 +1,2 @@
+export function problem(problem) { }
+void { problem: () => problem() };
diff --git a/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/options.json b/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/options.json
new file mode 100644
index 0000000000..0eae94b9f5
--- /dev/null
+++ b/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/options.json
@@ -0,0 +1,5 @@
+{
+  "plugins": [
+    "transform-function-name"
+  ]
+}
diff --git a/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/output.mjs b/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/output.mjs
new file mode 100644
index 0000000000..413c2b85c5
--- /dev/null
+++ b/packages/babel-traverse/test/fixtures/rename/property-rename-with-export/output.mjs
@@ -0,0 +1,6 @@
+function _problem(problem) {}
+
+export { _problem as problem };
+void {
+  problem: () => _problem()
+};