diff --git a/src/lightning/fabric/CHANGELOG.md b/src/lightning/fabric/CHANGELOG.md
index 18537ca15e2fc..2b1d651d1c027 100644
--- a/src/lightning/fabric/CHANGELOG.md
+++ b/src/lightning/fabric/CHANGELOG.md
@@ -21,6 +21,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Raise ValueError when seed is `out-of-bounds` or `cannot be cast to int` ([#21029](https://github.com/Lightning-AI/pytorch-lightning/pull/21029))
 
 
+- fix: remove extra `name` parameter in accelerator registry decorator ([#20975](https://github.com/Lightning-AI/pytorch-lightning/pull/20975))
+
+
 ---
 
 ## [2.5.2] - 2025-3-20
diff --git a/src/lightning/fabric/accelerators/registry.py b/src/lightning/fabric/accelerators/registry.py
index 4959a0fb9426a..539b7aa8a01dc 100644
--- a/src/lightning/fabric/accelerators/registry.py
+++ b/src/lightning/fabric/accelerators/registry.py
@@ -73,14 +73,14 @@ def register(
         data["description"] = description
         data["init_params"] = init_params
 
-        def do_register(name: str, accelerator: Callable) -> Callable:
+        def do_register(accelerator: Callable) -> Callable:
             data["accelerator"] = accelerator
             data["accelerator_name"] = name
             self[name] = data
             return accelerator
 
         if accelerator is not None:
-            return do_register(name, accelerator)
+            return do_register(accelerator)
 
         return do_register
 
diff --git a/tests/tests_fabric/accelerators/test_registry.py b/tests/tests_fabric/accelerators/test_registry.py
index 8036a6f45b8a0..b88ecf1db1e57 100644
--- a/tests/tests_fabric/accelerators/test_registry.py
+++ b/tests/tests_fabric/accelerators/test_registry.py
@@ -16,6 +16,38 @@
 import torch
 
 from lightning.fabric.accelerators import ACCELERATOR_REGISTRY, Accelerator
+from lightning.fabric.accelerators.registry import _AcceleratorRegistry
+
+
+class TestAccelerator(Accelerator):
+    """Helper accelerator class for testing."""
+
+    def __init__(self, param1=None, param2=None):
+        self.param1 = param1
+        self.param2 = param2
+        super().__init__()
+
+    def setup_device(self, device: torch.device) -> None:
+        pass
+
+    def teardown(self) -> None:
+        pass
+
+    @staticmethod
+    def parse_devices(devices):
+        return devices
+
+    @staticmethod
+    def get_parallel_devices(devices):
+        return ["foo"] * devices
+
+    @staticmethod
+    def auto_device_count():
+        return 3
+
+    @staticmethod
+    def is_available():
+        return True
 
 
 def test_accelerator_registry_with_new_accelerator():
@@ -71,3 +103,75 @@ def is_available():
 
 def test_available_accelerators_in_registry():
     assert ACCELERATOR_REGISTRY.available_accelerators() == {"cpu", "cuda", "mps", "tpu"}
+
+
+def test_registry_as_decorator():
+    """Test that the registry can be used as a decorator."""
+    test_registry = _AcceleratorRegistry()
+
+    # Test decorator usage
+    @test_registry.register("test_decorator", description="Test decorator accelerator", param1="value1", param2=42)
+    class DecoratorAccelerator(TestAccelerator):
+        pass
+
+    # Verify registration worked
+    assert "test_decorator" in test_registry
+    assert test_registry["test_decorator"]["description"] == "Test decorator accelerator"
+    assert test_registry["test_decorator"]["init_params"] == {"param1": "value1", "param2": 42}
+    assert test_registry["test_decorator"]["accelerator"] == DecoratorAccelerator
+    assert test_registry["test_decorator"]["accelerator_name"] == "test_decorator"
+
+    # Test that we can instantiate the accelerator
+    instance = test_registry.get("test_decorator")
+    assert isinstance(instance, DecoratorAccelerator)
+    assert instance.param1 == "value1"
+    assert instance.param2 == 42
+
+
+def test_registry_as_static_method():
+    """Test that the registry can be used as a static method call."""
+    test_registry = _AcceleratorRegistry()
+
+    class StaticMethodAccelerator(TestAccelerator):
+        pass
+
+    # Test static method usage
+    result = test_registry.register(
+        "test_static",
+        StaticMethodAccelerator,
+        description="Test static method accelerator",
+        param1="static_value",
+        param2=100,
+    )
+
+    # Verify registration worked
+    assert "test_static" in test_registry
+    assert test_registry["test_static"]["description"] == "Test static method accelerator"
+    assert test_registry["test_static"]["init_params"] == {"param1": "static_value", "param2": 100}
+    assert test_registry["test_static"]["accelerator"] == StaticMethodAccelerator
+    assert test_registry["test_static"]["accelerator_name"] == "test_static"
+    assert result == StaticMethodAccelerator  # Should return the accelerator class
+
+    # Test that we can instantiate the accelerator
+    instance = test_registry.get("test_static")
+    assert isinstance(instance, StaticMethodAccelerator)
+    assert instance.param1 == "static_value"
+    assert instance.param2 == 100
+
+
+def test_registry_without_parameters():
+    """Test registration without init parameters."""
+    test_registry = _AcceleratorRegistry()
+
+    class SimpleAccelerator(TestAccelerator):
+        def __init__(self):
+            super().__init__()
+
+    test_registry.register("simple", SimpleAccelerator, description="Simple accelerator")
+
+    assert "simple" in test_registry
+    assert test_registry["simple"]["description"] == "Simple accelerator"
+    assert test_registry["simple"]["init_params"] == {}
+
+    instance = test_registry.get("simple")
+    assert isinstance(instance, SimpleAccelerator)