Don't consider Union to always be a type alias

doc/whatsnew/fragments/8487.false_positive

@@ -0,0 +1,3 @@
+No longer consider ``Union`` as type annotation as type alias for naming checks.
+
+Closes #8487

pylint/checkers/base/name_checker/checker.py

@@ -597,6 +597,14 @@ def _assigns_typealias(node: nodes.NodeNG | None) -> bool:
         inferred = utils.safe_infer(node)
         if isinstance(inferred, nodes.ClassDef):
             if inferred.qname() == ".Union":
+                # Union is a special case because it can be used as a type alias
+                # or as a type annotation. We only want to check the former.
+                assert node is not None
+                if (
+                    isinstance(node.parent, nodes.AnnAssign)
+                    and node.parent.value is not None
+                ):
+                    return False
                 return True
         elif isinstance(inferred, nodes.FunctionDef):
             if inferred.qname() == "typing.TypeAlias":

tests/functional/t/typealias_naming_style_default.py

@@ -21,3 +21,7 @@
 _BAD_NAME = Union[int, str]  # [invalid-name]
 __BAD_NAME = Union[int, str]  # [invalid-name]
 ANOTHERBADNAME = Union[int, str]  # [invalid-name]
+
+# Regression tests
+# This is not a TypeAlias, and thus shouldn't flag the message
+x: Union[str, int] = 42