diff --git a/Doc/library/asyncio-eventloop.rst b/Doc/library/asyncio-eventloop.rst
index 92b98e2b2c862c..20b1ccd105109e 100644
--- a/Doc/library/asyncio-eventloop.rst
+++ b/Doc/library/asyncio-eventloop.rst
@@ -355,7 +355,7 @@ Creating Futures and Tasks
 
    .. versionadded:: 3.5.2
 
-.. method:: loop.create_task(coro, *, name=None, context=None)
+.. method:: loop.create_task(coro, *, name=None, context=None, **kwargs)
 
    Schedule the execution of :ref:`coroutine <coroutine>` *coro*.
    Return a :class:`Task` object.
@@ -364,6 +364,11 @@ Creating Futures and Tasks
    for interoperability. In this case, the result type is a subclass
    of :class:`Task`.
 
+   The full function signature is largely the same as that of the
+   :class:`Task` constructor (or factory) - all of the keyword arguments to
+   this function are passed through to that interface, except *name*,
+   or *context* if it is ``None``.
+
    If the *name* argument is provided and not ``None``, it is set as
    the name of the task using :meth:`Task.set_name`.
 
@@ -377,6 +382,13 @@ Creating Futures and Tasks
    .. versionchanged:: 3.11
       Added the *context* parameter.
 
+   .. versionchanged:: 3.13.3
+      Added ``kwargs`` which passes on arbitrary extra parameters, including  ``name`` and ``context``.
+
+   .. versionchanged:: 3.13.4
+      Rolled back the change that passes on *name* and *context* (if it is None),
+      while still passing on other arbitrary keyword arguments (to avoid breaking backwards compatibility with 3.13.3).
+
 .. method:: loop.set_task_factory(factory)
 
    Set a task factory that will be used by
@@ -388,6 +400,13 @@ Creating Futures and Tasks
    event loop, and *coro* is a coroutine object.  The callable
    must pass on all *kwargs*, and return a :class:`asyncio.Task`-compatible object.
 
+   .. versionchanged:: 3.13.3
+      Required that all *kwargs* are passed on to :class:`asyncio.Task`.
+
+   .. versionchanged:: 3.13.4
+      *name* is no longer passed to task factories. *context* is no longer passed
+      to task factories if it is ``None``.
+
 .. method:: loop.get_task_factory()
 
    Return a task factory or ``None`` if the default one is in use.
diff --git a/Lib/asyncio/base_events.py b/Lib/asyncio/base_events.py
index d2cedb68985853..07ec6de6414ec2 100644
--- a/Lib/asyncio/base_events.py
+++ b/Lib/asyncio/base_events.py
@@ -458,18 +458,24 @@ def create_future(self):
         """Create a Future object attached to the loop."""
         return futures.Future(loop=self)
 
-    def create_task(self, coro, **kwargs):
+    def create_task(self, coro, *, name=None, context=None, **kwargs):
         """Schedule a coroutine object.
 
         Return a task object.
         """
         self._check_closed()
         if self._task_factory is not None:
-            return self._task_factory(self, coro, **kwargs)
+            if context is not None:
+                kwargs["context"] = context
+
+            task = self._task_factory(self, coro, **kwargs)
+            task.set_name(name)
+
+        else:
+            task = tasks.Task(coro, loop=self, name=name, context=context, **kwargs)
+            if task._source_traceback:
+                del task._source_traceback[-1]
 
-        task = tasks.Task(coro, loop=self, **kwargs)
-        if task._source_traceback:
-            del task._source_traceback[-1]
         try:
             return task
         finally:
diff --git a/Lib/test/test_asyncio/test_taskgroups.py b/Lib/test/test_asyncio/test_taskgroups.py
index 9f2211e3232e54..ad61cb46c7c07c 100644
--- a/Lib/test/test_asyncio/test_taskgroups.py
+++ b/Lib/test/test_asyncio/test_taskgroups.py
@@ -1081,18 +1081,6 @@ async def throw_error():
         # cancellation happens here and error is more understandable
         await asyncio.sleep(0)
 
-    async def test_name(self):
-        name = None
-
-        async def asyncfn():
-            nonlocal name
-            name = asyncio.current_task().get_name()
-
-        async with asyncio.TaskGroup() as tg:
-            tg.create_task(asyncfn(), name="example name")
-
-        self.assertEqual(name, "example name")
-
 
 class TestTaskGroup(BaseTestTaskGroup, unittest.IsolatedAsyncioTestCase):
     loop_factory = asyncio.EventLoop
diff --git a/Misc/NEWS.d/next/Library/2025-05-14-08-13-08.gh-issue-133745.rjgJkH.rst b/Misc/NEWS.d/next/Library/2025-05-14-08-13-08.gh-issue-133745.rjgJkH.rst
new file mode 100644
index 00000000000000..78cc3d9cfa0ee7
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2025-05-14-08-13-08.gh-issue-133745.rjgJkH.rst
@@ -0,0 +1 @@
+In 3.13.3 we accidentally changed the signature of the asyncio ``create_task()`` family of methods and how it calls a custom task factory in a backwards incompatible way. Since some 3rd party libraries have already made changes to work around the issue that might break if we simply reverted the changes, we're instead changing things to be backwards compatible with 3.13.2 while still supporting those workarounds for 3.13.3. In particular, the special-casing of ``name`` and ``context`` is back (until 3.14) and consequently eager tasks may still find that their name hasn't been set before they execute their first yielding await.