diff --git a/fastapi/routing.py b/fastapi/routing.py
index 78207778a..0a971f98b 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -127,7 +127,7 @@ def request_response(
     async def app(scope: Scope, receive: Receive, send: Send) -> None:
         request = Request(scope, receive, send)
 
-        async def app(scope: Scope, receive: Receive, send: Send) -> None:
+        async def inner_app(scope: Scope, receive: Receive, send: Send) -> None:
             # Starts customization
             response_awaited = False
             async with AsyncExitStack() as request_stack:
@@ -148,7 +148,7 @@ def request_response(
                 )
 
         # Same as in Starlette
-        await wrap_app_handling_exceptions(app, request)(scope, receive, send)
+        await wrap_app_handling_exceptions(inner_app, request)(scope, receive, send)
 
     return app
 
@@ -166,7 +166,7 @@ def websocket_session(
     async def app(scope: Scope, receive: Receive, send: Send) -> None:
         session = WebSocket(scope, receive=receive, send=send)
 
-        async def app(scope: Scope, receive: Receive, send: Send) -> None:
+        async def inner_app(scope: Scope, receive: Receive, send: Send) -> None:
             async with AsyncExitStack() as request_stack:
                 scope["fastapi_inner_astack"] = request_stack
                 async with AsyncExitStack() as function_stack:
@@ -174,7 +174,7 @@ def websocket_session(
                     await func(session)
 
         # Same as in Starlette
-        await wrap_app_handling_exceptions(app, session)(scope, receive, send)
+        await wrap_app_handling_exceptions(inner_app, session)(scope, receive, send)
 
     return app