diff --git a/packages/babel-helper-function-name/src/index.ts b/packages/babel-helper-function-name/src/index.ts
index 16c3fcc6fad5..09dd4c61bd53 100644
--- a/packages/babel-helper-function-name/src/index.ts
+++ b/packages/babel-helper-function-name/src/index.ts
@@ -172,6 +172,7 @@ function visit(node, name, scope) {
 /**
  * @param {NodePath} param0
  * @param {Boolean} localBinding whether a name could shadow a self-reference (e.g. converting arrow function)
+ * @param {Boolean} supportUnicodeId whether a target support unicodeId or not
  */
 export default function (
   {
@@ -181,6 +182,7 @@ export default function (
     id,
   }: { node: any; parent?: any; scope: any; id?: any },
   localBinding = false,
+  supportUnicodeId = false,
 ) {
   // has an `id` so we don't need to infer one
   if (node.id) return;
@@ -227,6 +229,10 @@ export default function (
     return;
   }
 
+  if (!supportUnicodeId && isFunction(node) && /[\uD800-\uDFFF]/.test(name)) {
+    return;
+  }
+
   name = toBindingIdentifierName(name);
   id = identifier(name);
 
diff --git a/packages/babel-plugin-transform-function-name/package.json b/packages/babel-plugin-transform-function-name/package.json
index 6b1488370826..bdf9a5f7184c 100644
--- a/packages/babel-plugin-transform-function-name/package.json
+++ b/packages/babel-plugin-transform-function-name/package.json
@@ -17,6 +17,7 @@
     "babel-plugin"
   ],
   "dependencies": {
+    "@babel/helper-compilation-targets": "workspace:^",
     "@babel/helper-function-name": "workspace:^",
     "@babel/helper-plugin-utils": "workspace:^"
   },
diff --git a/packages/babel-plugin-transform-function-name/src/index.ts b/packages/babel-plugin-transform-function-name/src/index.ts
index 4c9c56f083e9..7bdae7fca350 100644
--- a/packages/babel-plugin-transform-function-name/src/index.ts
+++ b/packages/babel-plugin-transform-function-name/src/index.ts
@@ -1,8 +1,13 @@
+import { isRequired } from "@babel/helper-compilation-targets";
 import { declare } from "@babel/helper-plugin-utils";
 import nameFunction from "@babel/helper-function-name";
 
 export default declare(api => {
   api.assertVersion(7);
+  const supportUnicodeId = !isRequired(
+    "transform-unicode-escapes",
+    api.targets(),
+  );
 
   return {
     name: "transform-function-name",
@@ -20,7 +25,7 @@ export default declare(api => {
       ObjectProperty(path) {
         const value = path.get("value");
         if (value.isFunction()) {
-          const newNode = nameFunction(value);
+          const newNode = nameFunction(value, false, supportUnicodeId);
           if (newNode) value.replaceWith(newNode);
         }
       },
diff --git a/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/input.js b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/input.js
new file mode 100644
index 000000000000..1ce32e6bf532
--- /dev/null
+++ b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/input.js
@@ -0,0 +1,3 @@
+var o = {
+  "\uD835\uDC9C"() {}
+};
\ No newline at end of file
diff --git a/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/options.json b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/options.json
new file mode 100644
index 000000000000..0fc67a40d23e
--- /dev/null
+++ b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/options.json
@@ -0,0 +1,4 @@
+{
+    "plugins": ["transform-function-name", "transform-shorthand-properties"],
+    "targets": { "firefox": 52 }
+}
\ No newline at end of file
diff --git a/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/output.js b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/output.js
new file mode 100644
index 000000000000..bf365d536975
--- /dev/null
+++ b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-not-supported/output.js
@@ -0,0 +1,3 @@
+var o = {
+  "\uD835\uDC9C": function () {}
+};
diff --git a/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/input.js b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/input.js
new file mode 100644
index 000000000000..1ce32e6bf532
--- /dev/null
+++ b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/input.js
@@ -0,0 +1,3 @@
+var o = {
+  "\uD835\uDC9C"() {}
+};
\ No newline at end of file
diff --git a/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/options.json b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/options.json
new file mode 100644
index 000000000000..ed532b7396fc
--- /dev/null
+++ b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/options.json
@@ -0,0 +1,4 @@
+{
+    "plugins": ["transform-function-name", "transform-shorthand-properties"],
+    "targets": { "firefox": 60 }
+}
\ No newline at end of file
diff --git a/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/output.js b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/output.js
new file mode 100644
index 000000000000..9ef7f98005fe
--- /dev/null
+++ b/packages/babel-plugin-transform-function-name/test/fixtures/function-name/unicode-id-supported/output.js
@@ -0,0 +1,3 @@
+var o = {
+  "\uD835\uDC9C": function 𝒜() {}
+};
diff --git a/yarn.lock b/yarn.lock
index 437c47af55c8..7be8b34d2146 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -2438,6 +2438,7 @@ __metadata:
   resolution: "@babel/plugin-transform-function-name@workspace:packages/babel-plugin-transform-function-name"
   dependencies:
     "@babel/core": "workspace:^"
+    "@babel/helper-compilation-targets": "workspace:^"
     "@babel/helper-function-name": "workspace:^"
     "@babel/helper-plugin-test-runner": "workspace:^"
     "@babel/helper-plugin-utils": "workspace:^"