diff --git a/mypy/checker.py b/mypy/checker.py
index e727c343aa14..43b166b86f72 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -5875,7 +5875,7 @@ def check_subtype(
         if (
             isinstance(supertype, Instance)
             and supertype.type.is_protocol
-            and isinstance(subtype, (Instance, TupleType, TypedDictType))
+            and isinstance(subtype, (CallableType, Instance, TupleType, TypedDictType))
         ):
             self.msg.report_protocol_problems(subtype, supertype, context, code=msg.code)
         if isinstance(supertype, CallableType) and isinstance(subtype, Instance):
@@ -5883,10 +5883,11 @@ def check_subtype(
             if call:
                 self.msg.note_call(subtype, call, context, code=msg.code)
         if isinstance(subtype, (CallableType, Overloaded)) and isinstance(supertype, Instance):
-            if supertype.type.is_protocol and supertype.type.protocol_members == ["__call__"]:
+            if supertype.type.is_protocol and "__call__" in supertype.type.protocol_members:
                 call = find_member("__call__", supertype, subtype, is_operator=True)
                 assert call is not None
-                self.msg.note_call(supertype, call, context, code=msg.code)
+                if not is_subtype(subtype, call, options=self.options):
+                    self.msg.note_call(supertype, call, context, code=msg.code)
         self.check_possible_missing_await(subtype, supertype, context)
         return False
 
diff --git a/mypy/constraints.py b/mypy/constraints.py
index 2a641bf27ed5..7123c590b7ef 100644
--- a/mypy/constraints.py
+++ b/mypy/constraints.py
@@ -553,7 +553,7 @@ def visit_instance(self, template: Instance) -> list[Constraint]:
         original_actual = actual = self.actual
         res: list[Constraint] = []
         if isinstance(actual, (CallableType, Overloaded)) and template.type.is_protocol:
-            if template.type.protocol_members == ["__call__"]:
+            if "__call__" in template.type.protocol_members:
                 # Special case: a generic callback protocol
                 if not any(template == t for t in template.type.inferring):
                     template.type.inferring.append(template)
@@ -565,7 +565,6 @@ def visit_instance(self, template: Instance) -> list[Constraint]:
                         subres = infer_constraints(call, actual, self.direction)
                         res.extend(subres)
                     template.type.inferring.pop()
-                    return res
         if isinstance(actual, CallableType) and actual.fallback is not None:
             if actual.is_type_obj() and template.type.is_protocol:
                 ret_type = get_proper_type(actual.ret_type)
@@ -815,7 +814,7 @@ def visit_instance(self, template: Instance) -> list[Constraint]:
                 # because some type may be considered a subtype of a protocol
                 # due to _promote, but still not implement the protocol.
                 not any(template == t for t in reversed(template.type.inferring))
-                and mypy.subtypes.is_protocol_implementation(instance, erased)
+                and mypy.subtypes.is_protocol_implementation(instance, erased, skip=["__call__"])
             ):
                 template.type.inferring.append(template)
                 res.extend(
@@ -831,7 +830,7 @@ def visit_instance(self, template: Instance) -> list[Constraint]:
                 and
                 # We avoid infinite recursion for structural subtypes also here.
                 not any(instance == i for i in reversed(instance.type.inferring))
-                and mypy.subtypes.is_protocol_implementation(erased, instance)
+                and mypy.subtypes.is_protocol_implementation(erased, instance, skip=["__call__"])
             ):
                 instance.type.inferring.append(instance)
                 res.extend(
@@ -887,6 +886,8 @@ def infer_constraints_from_protocol_members(
             inst = mypy.subtypes.find_member(member, instance, subtype, class_obj=class_obj)
             temp = mypy.subtypes.find_member(member, template, subtype)
             if inst is None or temp is None:
+                if member == "__call__":
+                    continue
                 return []  # See #11020
             # The above is safe since at this point we know that 'instance' is a subtype
             # of (erased) 'template', therefore it defines all protocol members
diff --git a/mypy/messages.py b/mypy/messages.py
index e11ee9d0f7f2..75871d9b5521 100644
--- a/mypy/messages.py
+++ b/mypy/messages.py
@@ -1866,6 +1866,7 @@ def report_protocol_problems(
 
         class_obj = False
         is_module = False
+        skip = []
         if isinstance(subtype, TupleType):
             if not isinstance(subtype.partial_fallback, Instance):
                 return
@@ -1880,20 +1881,22 @@ def report_protocol_problems(
             class_obj = True
             subtype = subtype.item
         elif isinstance(subtype, CallableType):
-            if not subtype.is_type_obj():
-                return
-            ret_type = get_proper_type(subtype.ret_type)
-            if isinstance(ret_type, TupleType):
-                ret_type = ret_type.partial_fallback
-            if not isinstance(ret_type, Instance):
-                return
-            class_obj = True
-            subtype = ret_type
+            if subtype.is_type_obj():
+                ret_type = get_proper_type(subtype.ret_type)
+                if isinstance(ret_type, TupleType):
+                    ret_type = ret_type.partial_fallback
+                if not isinstance(ret_type, Instance):
+                    return
+                class_obj = True
+                subtype = ret_type
+            else:
+                subtype = subtype.fallback
+                skip = ["__call__"]
         if subtype.extra_attrs and subtype.extra_attrs.mod_name:
             is_module = True
 
         # Report missing members
-        missing = get_missing_protocol_members(subtype, supertype)
+        missing = get_missing_protocol_members(subtype, supertype, skip=skip)
         if (
             missing
             and len(missing) < len(supertype.type.protocol_members)
@@ -2605,13 +2608,15 @@ def variance_string(variance: int) -> str:
         return "invariant"
 
 
-def get_missing_protocol_members(left: Instance, right: Instance) -> list[str]:
+def get_missing_protocol_members(left: Instance, right: Instance, skip: list[str]) -> list[str]:
     """Find all protocol members of 'right' that are not implemented
     (i.e. completely missing) in 'left'.
     """
     assert right.type.is_protocol
     missing: list[str] = []
     for member in right.type.protocol_members:
+        if member in skip:
+            continue
         if not find_member(member, left, left):
             missing.append(member)
     return missing
diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index 9a4982f5b8ec..f928e1cc7918 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -678,13 +678,16 @@ def visit_callable_type(self, left: CallableType) -> bool:
         elif isinstance(right, Overloaded):
             return all(self._is_subtype(left, item) for item in right.items)
         elif isinstance(right, Instance):
-            if right.type.is_protocol and right.type.protocol_members == ["__call__"]:
-                # OK, a callable can implement a protocol with a single `__call__` member.
+            if right.type.is_protocol and "__call__" in right.type.protocol_members:
+                # OK, a callable can implement a protocol with a `__call__` member.
                 # TODO: we should probably explicitly exclude self-types in this case.
                 call = find_member("__call__", right, left, is_operator=True)
                 assert call is not None
                 if self._is_subtype(left, call):
-                    return True
+                    if len(right.type.protocol_members) == 1:
+                        return True
+                    if is_protocol_implementation(left.fallback, right, skip=["__call__"]):
+                        return True
             if right.type.is_protocol and left.is_type_obj():
                 ret_type = get_proper_type(left.ret_type)
                 if isinstance(ret_type, TupleType):
@@ -792,12 +795,15 @@ def visit_literal_type(self, left: LiteralType) -> bool:
     def visit_overloaded(self, left: Overloaded) -> bool:
         right = self.right
         if isinstance(right, Instance):
-            if right.type.is_protocol and right.type.protocol_members == ["__call__"]:
+            if right.type.is_protocol and "__call__" in right.type.protocol_members:
                 # same as for CallableType
                 call = find_member("__call__", right, left, is_operator=True)
                 assert call is not None
                 if self._is_subtype(left, call):
-                    return True
+                    if len(right.type.protocol_members) == 1:
+                        return True
+                    if is_protocol_implementation(left.fallback, right, skip=["__call__"]):
+                        return True
             return self._is_subtype(left.fallback, right)
         elif isinstance(right, CallableType):
             for item in left.items:
@@ -938,7 +944,11 @@ def pop_on_exit(stack: list[tuple[T, T]], left: T, right: T) -> Iterator[None]:
 
 
 def is_protocol_implementation(
-    left: Instance, right: Instance, proper_subtype: bool = False, class_obj: bool = False
+    left: Instance,
+    right: Instance,
+    proper_subtype: bool = False,
+    class_obj: bool = False,
+    skip: list[str] | None = None,
 ) -> bool:
     """Check whether 'left' implements the protocol 'right'.
 
@@ -958,10 +968,13 @@ def f(self) -> A: ...
     as well.
     """
     assert right.type.is_protocol
+    if skip is None:
+        skip = []
     # We need to record this check to generate protocol fine-grained dependencies.
     TypeState.record_protocol_subtype_check(left.type, right.type)
     # nominal subtyping currently ignores '__init__' and '__new__' signatures
     members_not_to_check = {"__init__", "__new__"}
+    members_not_to_check.update(skip)
     # Trivial check that circumvents the bug described in issue 9771:
     if left.type.is_protocol:
         members_right = set(right.type.protocol_members) - members_not_to_check
diff --git a/mypy/test/testtypegen.py b/mypy/test/testtypegen.py
index db155a337980..22ef4272e933 100644
--- a/mypy/test/testtypegen.py
+++ b/mypy/test/testtypegen.py
@@ -7,7 +7,7 @@
 from mypy import build
 from mypy.errors import CompileError
 from mypy.modulefinder import BuildSource
-from mypy.nodes import NameExpr
+from mypy.nodes import NameExpr, TempNode
 from mypy.options import Options
 from mypy.test.config import test_temp_dir
 from mypy.test.data import DataDrivenTestCase, DataSuite
@@ -54,6 +54,8 @@ def run_case(self, testcase: DataDrivenTestCase) -> None:
             # Filter nodes that should be included in the output.
             keys = []
             for node in nodes:
+                if isinstance(node, TempNode):
+                    continue
                 if node.line != -1 and map[node]:
                     if ignore_node(node) or node in ignored:
                         continue
diff --git a/test-data/unit/check-protocols.test b/test-data/unit/check-protocols.test
index 113b2000fc22..77c14b92b261 100644
--- a/test-data/unit/check-protocols.test
+++ b/test-data/unit/check-protocols.test
@@ -2642,6 +2642,53 @@ reveal_type([b, a])  # N: Revealed type is "builtins.list[def (x: def (__main__.
 [builtins fixtures/list.pyi]
 [out]
 
+[case testCallbackProtocolFunctionAttributesSubtyping]
+from typing import Protocol
+
+class A(Protocol):
+    __name__: str
+    def __call__(self) -> str: ...
+
+class B1(Protocol):
+    __name__: int
+    def __call__(self) -> str: ...
+
+class B2(Protocol):
+    __name__: str
+    def __call__(self) -> int: ...
+
+class B3(Protocol):
+    __name__: str
+    extra_stuff: int
+    def __call__(self) -> str: ...
+
+def f() -> str: ...
+
+reveal_type(f.__name__)  # N: Revealed type is "builtins.str"
+a: A = f  # OK
+b1: B1 = f  # E: Incompatible types in assignment (expression has type "Callable[[], str]", variable has type "B1") \
+            # N: Following member(s) of "function" have conflicts: \
+            # N:     __name__: expected "int", got "str"
+b2: B2 = f  # E: Incompatible types in assignment (expression has type "Callable[[], str]", variable has type "B2") \
+            # N: "B2.__call__" has type "Callable[[], int]"
+b3: B3 = f  # E: Incompatible types in assignment (expression has type "Callable[[], str]", variable has type "B3") \
+            # N: "function" is missing following "B3" protocol member: \
+            # N:     extra_stuff
+
+[case testCallbackProtocolFunctionAttributesInference]
+from typing import Protocol, TypeVar, Generic, Tuple
+
+T = TypeVar("T")
+S = TypeVar("S", covariant=True)
+class A(Protocol[T, S]):
+    __name__: T
+    def __call__(self) -> S: ...
+
+def f() -> int: ...
+def test(func: A[T, S]) -> Tuple[T, S]: ...
+reveal_type(test(f))  # N: Revealed type is "Tuple[builtins.str, builtins.int]"
+[builtins fixtures/tuple.pyi]
+
 [case testProtocolsAlwaysABCs]
 from typing import Protocol
 
diff --git a/test-data/unit/fine-grained-inspect.test b/test-data/unit/fine-grained-inspect.test
index a52db3959633..8574477d8272 100644
--- a/test-data/unit/fine-grained-inspect.test
+++ b/test-data/unit/fine-grained-inspect.test
@@ -52,8 +52,8 @@ class Meta(type):
 ==
 {"C": ["meth", "x"]}
 {"C": ["meth", "x"], "Meta": ["y"], "type": ["__init__"]}
-{}
-{"object": ["__init__"]}
+{"function": ["__name__"]}
+{"function": ["__name__"], "object": ["__init__"]}
 
 [case testInspectDefBasic]
 # inspect2: --show=definition foo.py:5:5
diff --git a/test-data/unit/fixtures/tuple.pyi b/test-data/unit/fixtures/tuple.pyi
index 5c69a4ad1eb5..14e668375175 100644
--- a/test-data/unit/fixtures/tuple.pyi
+++ b/test-data/unit/fixtures/tuple.pyi
@@ -23,7 +23,8 @@ class tuple(Sequence[Tco], Generic[Tco]):
     def __rmul__(self, n: int) -> Tuple[Tco, ...]: pass
     def __add__(self, x: Tuple[Tco, ...]) -> Tuple[Tco, ...]: pass
     def count(self, obj: object) -> int: pass
-class function: pass
+class function:
+    __name__: str
 class ellipsis: pass
 class classmethod: pass
 
diff --git a/test-data/unit/lib-stub/builtins.pyi b/test-data/unit/lib-stub/builtins.pyi
index 8c4f504fb2e7..82e0f6135614 100644
--- a/test-data/unit/lib-stub/builtins.pyi
+++ b/test-data/unit/lib-stub/builtins.pyi
@@ -17,7 +17,8 @@ class float: pass
 class str: pass
 class bytes: pass
 
-class function: pass
+class function:
+    __name__: str
 class ellipsis: pass
 
 from typing import Generic, Sequence, TypeVar