Fix task execution for tools with custom names

When a tool was registered with a custom name different from its function
name, task execution would fail because Docket registered the function by
its `__name__` but the handler looked it up by the tool's configured name.

This switches to using Docket's new `names=` parameter (pydocket 0.16.0)
to register functions with their proper lookup keys, and removes the
`_create_named_fn_wrapper` hack that was used for mounted servers.

Closes #2642

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

tests/server/tasks/test_server_tasks_parameter.py

@@ -308,3 +308,29 @@ async def test_multiple_components_same_name_different_tasks():
         # Prompt inheriting False (mode="forbidden") raises McpError
         with pytest.raises(McpError):
             await client.get_prompt("shared_name_prompt", task=True)
+
+
+async def test_task_with_custom_tool_name():
+    """Tools with custom names work correctly as tasks (issue #2642).
+
+    When a tool is registered with a custom name different from the function
+    name, task execution should use the custom name for Docket lookup.
+    """
+    mcp = FastMCP("test", tasks=True)
+
+    async def my_function() -> str:
+        return "result from custom-named tool"
+
+    mcp.tool(my_function, name="custom-tool-name")
+
+    async with Client(mcp) as client:
+        # Verify the tool is registered with its custom name in Docket
+        docket = mcp.docket
+        assert docket is not None
+        assert "custom-tool-name" in docket.tasks
+
+        # Call the tool as a task using its custom name
+        task = await client.call_tool("custom-tool-name", task=True)
+        assert not task.returned_immediately
+        result = await task
+        assert result.data == "result from custom-named tool"