[Backport maintenance/4.0.x] Fix FP for invalid-name with typing.Annotated

doc/whatsnew/fragments/10696.false_positive

@@ -0,0 +1,3 @@
+Fixed false positive for ``invalid-name`` with ``typing.Annotated``.
+
+Closes #10696

pylint/checkers/base/name_checker/checker.py

@@ -488,17 +488,7 @@ def visit_assignname(  # pylint: disable=too-many-branches,too-many-statements
                     return
 
                 # Check classes (TypeVar's are classes so they need to be excluded first)
-                elif isinstance(inferred_assign_type, nodes.ClassDef) or (
-                    isinstance(inferred_assign_type, bases.Instance)
-                    and {"EnumMeta", "TypedDict"}.intersection(
-                        {
-                            ancestor.name
-                            for ancestor in cast(
-                                InferenceResult, inferred_assign_type
-                            ).mro()
-                        }
-                    )
-                ):
+                elif self._should_check_class_regex(inferred_assign_type):
                     self._check_name("class", node.name, node)
 
                 # Don't emit if the name redefines an import in an ImportError except handler
@@ -576,6 +566,28 @@ def _meets_exception_for_non_consts(
         regexp = self._name_regexps["variable"]
         return regexp.match(name) is not None
 
+    def _should_check_class_regex(
+        self, inferred_assign_type: InferenceResult | None
+    ) -> bool:
+        if isinstance(inferred_assign_type, nodes.ClassDef):
+            return True
+        if isinstance(inferred_assign_type, bases.Instance) and {
+            "EnumMeta",
+            "TypedDict",
+        }.intersection(
+            {
+                ancestor.name
+                for ancestor in cast(InferenceResult, inferred_assign_type).mro()
+            }
+        ):
+            return True
+        if (
+            isinstance(inferred_assign_type, nodes.FunctionDef)
+            and inferred_assign_type.qname() == "typing.Annotated"
+        ):
+            return True
+        return False
+
     def _recursive_check_names(self, args: list[nodes.AssignName]) -> None:
         """Check names in a possibly recursive list <arg>."""
         for arg in args:

tests/functional/i/invalid/invalid_name/invalid_name_module_level.py

@@ -51,3 +51,7 @@ def A():  # [invalid-name]
     VERSION = version("ty")  # uninferable
 except PackageNotFoundError:
     VERSION = "0.0.0"
+
+
+from typing import Annotated
+IntWithAnnotation = Annotated[int, "anything"]