diff --git a/mmengine/optim/optimizer/builder.py b/mmengine/optim/optimizer/builder.py
index 013fa2f3af..7b4090ba7a 100644
--- a/mmengine/optim/optimizer/builder.py
+++ b/mmengine/optim/optimizer/builder.py
@@ -27,7 +27,7 @@ def register_torch_optimizers() -> List[str]:
                                                   torch.optim.Optimizer):
             if module_name == 'Adafactor':
                 OPTIMIZERS.register_module(
-                    name='torch_Adafactor', module=_optim)
+                    name='TorchAdafactor', module=_optim)
             else:
                 OPTIMIZERS.register_module(module=_optim)
             torch_optimizers.append(module_name)
diff --git a/mmengine/registry/build_functions.py b/mmengine/registry/build_functions.py
index 4fee07569a..fe907c80db 100644
--- a/mmengine/registry/build_functions.py
+++ b/mmengine/registry/build_functions.py
@@ -238,11 +238,12 @@ def build_optimizer_from_cfg(
         cfg: Union[dict, ConfigDict, Config],
         registry: Registry,
         default_args: Optional[Union[dict, ConfigDict, Config]] = None) -> Any:
-    if 'Adafactor' == cfg['type'] and digit_version(
-            torch.__version__) >= digit_version('2.5.0'):
-        from ..logging import print_log
+    from ..logging import print_log
+    if 'type' in cfg \
+            and 'Adafactor' == cfg['type'] \
+            and digit_version(torch.__version__) >= digit_version('2.5.0'):
         print_log(
-            'the torch version of Adafactor is registered as torch_Adafactor')
+            'the torch version of Adafactor is registered as TorchAdafactor')
     return build_from_cfg(cfg, registry, default_args)