diff --git a/packages/babel-plugin-transform-es2015-block-scoping/src/index.js b/packages/babel-plugin-transform-es2015-block-scoping/src/index.js
index 727a66e3b1..de3c63e699 100644
--- a/packages/babel-plugin-transform-es2015-block-scoping/src/index.js
+++ b/packages/babel-plugin-transform-es2015-block-scoping/src/index.js
@@ -90,9 +90,10 @@ function convertBlockScopedToVar(path, parent, scope, moveBindingsToParent = fal
     const parentScope = scope.getFunctionParent();
     const ids = path.getBindingIdentifiers();
     for (let name in ids) {
-      scope.removeOwnBinding(name);
+      let binding = scope.getOwnBinding(name);
+      if (binding) binding.kind = "var";
+      scope.moveBindingTo(name, parentScope);
     }
-    parentScope.registerBinding("var", path);
   }
 }
 
@@ -351,7 +352,6 @@ class BlockScoping {
       const binding = scope.getBinding(ref.name);
       if (!binding) continue;
       if (binding.kind === "let" || binding.kind === "const") {
-        scope.removeOwnBinding(ref.name);
         parentScope.registerBinding("var", binding.path);
       }
     }
diff --git a/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/actual.js b/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/actual.js
new file mode 100644
index 0000000000..85d943cd3b
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/actual.js
@@ -0,0 +1,5 @@
+let foo = () => {
+  foo = () => { };
+};
+
+foo();
diff --git a/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/expected.js b/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/expected.js
new file mode 100644
index 0000000000..3cd5698f0f
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/expected.js
@@ -0,0 +1,5 @@
+var _foo = function foo() {
+  _foo = function foo() {};
+};
+
+_foo();
diff --git a/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/options.json b/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/options.json
new file mode 100644
index 0000000000..38472510f3
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-block-scoping/test/fixtures/general/function-name/options.json
@@ -0,0 +1,7 @@
+{
+  "plugins": [
+    "transform-es2015-arrow-functions",
+    "transform-es2015-function-name",
+    "transform-es2015-block-scoping"
+  ]
+}