diff --git a/mypy/stubtest.py b/mypy/stubtest.py
index 89af8e465464..a0f886106715 100644
--- a/mypy/stubtest.py
+++ b/mypy/stubtest.py
@@ -654,10 +654,10 @@ def _verify_arg_name(
     if is_dunder(function_name, exclude_special=True):
         return
 
-    def strip_prefix(s: str, prefix: str) -> str:
-        return s.removeprefix(prefix)
-
-    if strip_prefix(stub_arg.variable.name, "__") == runtime_arg.name:
+    if (
+        stub_arg.variable.name == runtime_arg.name
+        or stub_arg.variable.name.removeprefix("__") == runtime_arg.name
+    ):
         return
 
     nonspecific_names = {"object", "args"}
@@ -948,6 +948,7 @@ def _verify_signature(
         if (
             runtime_arg.kind != inspect.Parameter.POSITIONAL_ONLY
             and (stub_arg.pos_only or stub_arg.variable.name.startswith("__"))
+            and not runtime_arg.name.startswith("__")
             and stub_arg.variable.name.strip("_") != "self"
             and not is_dunder(function_name, exclude_special=True)  # noisy for dunder methods
         ):
diff --git a/mypy/test/teststubtest.py b/mypy/test/teststubtest.py
index 099e7605eea2..492897d33a4a 100644
--- a/mypy/test/teststubtest.py
+++ b/mypy/test/teststubtest.py
@@ -339,6 +339,21 @@ def __exit__(self, exc_type, exc_val, exc_tb): pass
             """,
             error=None,
         )
+        yield Case(
+            stub="""def dunder_name(__x: int) -> None: ...""",
+            runtime="""def dunder_name(__x: int) -> None: ...""",
+            error=None,
+        )
+        yield Case(
+            stub="""def dunder_name_posonly(__x: int, /) -> None: ...""",
+            runtime="""def dunder_name_posonly(__x: int) -> None: ...""",
+            error=None,
+        )
+        yield Case(
+            stub="""def dunder_name_bad(x: int) -> None: ...""",
+            runtime="""def dunder_name_bad(__x: int) -> None: ...""",
+            error="dunder_name_bad",
+        )
 
     @collect_cases
     def test_arg_kind(self) -> Iterator[Case]: