diff --git a/starlette/routing.py b/starlette/routing.py
index 0388304c9..ea6ec2117 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -84,7 +84,7 @@ async def app(scope: Scope, receive: Receive, send: Send) -> None:
 
 
 def get_name(endpoint: typing.Callable) -> str:
-    if inspect.isfunction(endpoint) or inspect.isclass(endpoint):
+    if inspect.isroutine(endpoint) or inspect.isclass(endpoint):
         return endpoint.__name__
     return endpoint.__class__.__name__
 
diff --git a/tests/test_routing.py b/tests/test_routing.py
index 7077c5616..e8adaca48 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -1,4 +1,5 @@
 import functools
+import typing
 import uuid
 
 import pytest
@@ -710,3 +711,38 @@ def test_duplicated_param_names():
         match="Duplicated param names id, name at path /{id}/{name}/{id}/{name}",
     ):
         Route("/{id}/{name}/{id}/{name}", user)
+
+
+class Endpoint:
+    async def my_method(self, request):
+        ...  # pragma: no cover
+
+    @classmethod
+    async def my_classmethod(cls, request):
+        ...  # pragma: no cover
+
+    @staticmethod
+    async def my_staticmethod(request):
+        ...  # pragma: no cover
+
+    def __call__(self, request):
+        ...  # pragma: no cover
+
+
+@pytest.mark.parametrize(
+    "endpoint, expected_name",
+    [
+        pytest.param(func_homepage, "func_homepage", id="function"),
+        pytest.param(Endpoint().my_method, "my_method", id="method"),
+        pytest.param(Endpoint.my_classmethod, "my_classmethod", id="classmethod"),
+        pytest.param(
+            Endpoint.my_staticmethod,
+            "my_staticmethod",
+            id="staticmethod",
+        ),
+        pytest.param(Endpoint(), "Endpoint", id="object"),
+        pytest.param(lambda request: ..., "<lambda>", id="lambda"),
+    ],
+)
+def test_route_name(endpoint: typing.Callable, expected_name: str):
+    assert Route(path="/", endpoint=endpoint).name == expected_name