diff --git a/mypy/stubtest.py b/mypy/stubtest.py
index 4a38939a0390..61587469b5a6 100644
--- a/mypy/stubtest.py
+++ b/mypy/stubtest.py
@@ -1574,14 +1574,14 @@ def apply_decorator_to_funcitem(
         ):
             return func
         if decorator.fullname == "builtins.classmethod":
-            if func.arguments[0].variable.name not in ("_cls", "cls", "mcs", "metacls"):
-                raise StubtestFailure(
-                    f"unexpected class parameter name {func.arguments[0].variable.name!r} "
-                    f"in {dec.fullname}"
-                )
+            if not func.arguments or func.arguments[0].kind not in (nodes.ARG_POS, nodes.ARG_OPT):
+                # Nothing to drop, e.g. `def f(*args)`. inspect.signature of the runtime
+                # classmethod keeps the star argument too, so the two already line up.
+                return func
             # FuncItem is written so that copy.copy() actually works, even when compiled
             ret = copy.copy(func)
-            # Remove the cls argument, since it's not present in inspect.signature of classmethods
+            # Remove the cls argument, since it's not present in inspect.signature of classmethods.
+            # It can be given any name, so don't look at the name to decide.
             ret.arguments = ret.arguments[1:]
             return ret
         # Just give up on any other decorators. After excluding properties, we don't run into
diff --git a/mypy/test/teststubtest.py b/mypy/test/teststubtest.py
index 2b54a150892b..24ce57942966 100644
--- a/mypy/test/teststubtest.py
+++ b/mypy/test/teststubtest.py
@@ -682,6 +682,33 @@ def __new__(cls, *args, **kwargs): pass
             """,
             error=None,
         )
+        # The first parameter of a classmethod can be called anything, see #16583
+        yield Case(
+            stub="""
+            class GoodOddClsName:
+                @classmethod
+                def f(GoodOddClsName, number: int) -> None: ...
+            """,
+            runtime="""
+            class GoodOddClsName:
+                @classmethod
+                def f(GoodOddClsName, number): pass
+            """,
+            error=None,
+        )
+        yield Case(
+            stub="""
+            class GoodStarArgsCls:
+                @classmethod
+                def f(*args: int) -> None: ...
+            """,
+            runtime="""
+            class GoodStarArgsCls:
+                @classmethod
+                def f(*args): pass
+            """,
+            error=None,
+        )
 
     @collect_cases
     def test_arg_mismatch(self) -> Iterator[Case]: