pydantic
diff --git a/‎pydantic/_internal/_utils.py‎
Lines changed: 3 additions & 1 deletion b/‎pydantic/_internal/_utils.py‎
Lines changed: 3 additions & 1 deletion
diff --git a/‎tests/test_deprecated.py‎
Lines changed: 2 additions & 2 deletions b/‎tests/test_deprecated.py‎
Lines changed: 2 additions & 2 deletions
@@ -7,6 +7,7 @@
 
 import dataclasses
 import keyword
+import sys
 import typing
 import warnings
 import weakref
@@ -420,8 +421,9 @@ def __get__(self, instance: None, objtype: type[_ModelT]) -> _RT: ...
     def __get__(self, instance: _ModelT, objtype: type[_ModelT]) -> _RT: ...
     def __get__(self, instance: _ModelT | None, objtype: type[_ModelT]) -> _RT:
         if instance is not None:
+            attr_name = self.fget.__name__ if sys.version_info >= (3, 10) else self.fget.__func__.__name__
             warnings.warn(
-                'Accessing this attribute on the instance is deprecated, and will be removed in Pydantic V3. '
+                f'Accessing the {attr_name!r} attribute on the instance is deprecated. '
                 'Instead, you should access this attribute from the model class.',
                 category=PydanticDeprecatedSince211,
                 stacklevel=2,
 
@@ -330,10 +330,10 @@ def area(self) -> int:
     m = Model(x=1)
     assert len(Model.model_fields) == 2
 
-    with pytest.warns(PydanticDeprecatedSince211):
+    with pytest.warns(PydanticDeprecatedSince211, match="Accessing the 'model_fields' attribute"):
         assert len(m.model_fields) == 2
 
-    with pytest.warns(PydanticDeprecatedSince211):
+    with pytest.warns(PydanticDeprecatedSince211, match="Accessing the 'model_computed_fields' attribute"):
         assert len(m.model_computed_fields) == 1
 
     match = '^The `__fields__` attribute is deprecated, use `model_fields` instead.'