diff --git a/libs/babel-transform-react-display-name/index.js b/libs/babel-transform-react-display-name/index.js
index 274d02a6ea..b9a70dddc9 100644
--- a/libs/babel-transform-react-display-name/index.js
+++ b/libs/babel-transform-react-display-name/index.js
@@ -54,9 +54,14 @@ module.exports = function ({ types: t }) {
 
         if (!isExpressionFn) return
 
+        // Should only apply to top level components
+        const parentStatement = componentFn.getStatementParent()
+        if (!t.isProgram(parentStatement.parent)) {
+          return
+        }
+
         const declarator = componentFn.findParent((path) => t.isVariableDeclarator(path))
         if (declarator) {
-          const parentStatement = componentFn.getStatementParent()
           const name = declarator.node.id.name
           parentStatement.insertAfter(genDisplayName(path, name))
           return
@@ -66,11 +71,10 @@ module.exports = function ({ types: t }) {
           t.isAssignmentExpression(path)
         )
         if (assignmentExpression) {
-          const parentStatement = componentFn.getStatementParent()
           const leftHandSide = assignmentExpression.node.left
 
-          // Only want to do this step for top level components
-          if (!t.isProgram(parentStatement.parent) || !t.isMemberExpression(leftHandSide)) {
+          // Don't add display names to nested member expressions
+          if (!t.isMemberExpression(leftHandSide)) {
             return
           }
 
diff --git a/libs/babel-transform-react-display-name/index.spec.tsx b/libs/babel-transform-react-display-name/index.spec.tsx
index 6798abf1a8..d6db45e473 100644
--- a/libs/babel-transform-react-display-name/index.spec.tsx
+++ b/libs/babel-transform-react-display-name/index.spec.tsx
@@ -185,6 +185,29 @@ describe('classed template tag literals', () => {
   })
 })
 
+describe('cases that should not be transformed', () => {
+  it('should not transform a non-top level JSX function', () => {
+    const result = transform`
+      export function f() {
+        const nestedComponent = () => <div/> 
+      }
+    `
+
+    expect(result).toMatchInlineSnapshot(`
+      "\\"use strict\\";
+
+      Object.defineProperty(exports, \\"__esModule\\", {
+        value: true
+      });
+      exports.f = f;
+
+      function f() {
+        const nestedComponent = () => /*#__PURE__*/React.createElement(\\"div\\", null);
+      }"
+    `)
+  })
+})
+
 /**
  * Helper to streamline babel transforms
  */