diff --git a/changes/4407-tlambert03.md b/changes/4407-tlambert03.md
index e315bb1487..a4b567399d 100644
--- a/changes/4407-tlambert03.md
+++ b/changes/4407-tlambert03.md
@@ -1 +1 @@
-Fix PEP487 protocol in `BaseModel`: call `__set_name__` on namespace values that implement the method.
+Fix PEP487 `__set_name__` protocol in `BaseModel` for PrivateAttrs.
diff --git a/pydantic/main.py b/pydantic/main.py
index 0490216d7a..6c1eaf8ee4 100644
--- a/pydantic/main.py
+++ b/pydantic/main.py
@@ -287,10 +287,12 @@ def is_untouched(v: Any) -> bool:
             cls.__try_update_forward_refs__()
 
         # preserve `__set_name__` protocol defined in https://peps.python.org/pep-0487
+        # for attributes not in `new_namespace` (e.g. private attributes)
         for name, obj in namespace.items():
-            set_name = getattr(obj, '__set_name__', None)
-            if callable(set_name):
-                set_name(cls, name)
+            if name not in new_namespace:
+                set_name = getattr(obj, '__set_name__', None)
+                if callable(set_name):
+                    set_name(cls, name)
 
         return cls
 
diff --git a/tests/test_create_model.py b/tests/test_create_model.py
index 21c96e20fd..42387d5b7a 100644
--- a/tests/test_create_model.py
+++ b/tests/test_create_model.py
@@ -225,10 +225,11 @@ class TestGenericModel(GenericModel):
     assert result.__config__.orm_mode is True
 
 
-def test_set_name():
+@pytest.mark.parametrize('base', [ModelPrivateAttr, object])
+def test_set_name(base):
     calls = []
 
-    class class_deco(ModelPrivateAttr):
+    class class_deco(base):
         def __init__(self, fn):
             super().__init__()
             self.fn = fn
@@ -236,9 +237,22 @@ def __init__(self, fn):
         def __set_name__(self, owner, name):
             calls.append((owner, name))
 
+        def __get__(self, obj, type=None):
+            return self.fn(obj) if obj else self
+
     class A(BaseModel):
+        x: int
+
         @class_deco
         def _some_func(self):
-            return self
+            return self.x
 
     assert calls == [(A, '_some_func')]
+    a = A(x=2)
+
+    # we don't test whether calling the method on a PrivateAttr works:
+    # attribute access on privateAttributes is more complicated, it doesn't
+    # get added to the class namespace (and will also get set on the instance
+    # with _init_private_attributes), so the descriptor protocol won't work.
+    if base is object:
+        assert a._some_func == 2