diff --git a/src/structlog/_output.py b/src/structlog/_output.py
index b1612de6..da5495cf 100644
--- a/src/structlog/_output.py
+++ b/src/structlog/_output.py
@@ -256,13 +256,17 @@ class BytesLogger:
     .. versionadded:: 20.2.0
     """
 
-    __slots__ = ("_file", "_flush", "_lock", "_write")
+    __slots__ = ("_file", "_flush", "_lock", "_write", "name")
 
-    def __init__(self, file: BinaryIO | None = None):
+    def __init__(
+        self, file: BinaryIO | None = None, *, name: str | None = None
+    ):
         self._file = file or sys.stdout.buffer
         self._write = self._file.write
         self._flush = self._file.flush
 
+        self.name = name
+
         self._lock = _get_lock_for_file(self._file)
 
     def __getstate__(self) -> str:
@@ -345,4 +349,4 @@ def __init__(self, file: BinaryIO | None = None):
         self._file = file
 
     def __call__(self, *args: Any) -> BytesLogger:
-        return BytesLogger(self._file)
+        return BytesLogger(self._file, name=args[0] if args else None)
diff --git a/tests/test_output.py b/tests/test_output.py
index 8553aad9..c298dd9d 100644
--- a/tests/test_output.py
+++ b/tests/test_output.py
@@ -295,6 +295,22 @@ def test_deepcopy(self, capsys):
         assert "hello\n" == out
         assert "" == err
 
+    def test_name_attribute(self):
+        """
+        BytesLogger accepts a name keyword argument.
+        """
+        bl = BytesLogger(name="test_logger")
+
+        assert "test_logger" == bl.name
+
+    def test_name_defaults_to_none(self):
+        """
+        BytesLogger name defaults to None when not provided.
+        """
+        bl = BytesLogger()
+
+        assert bl.name is None
+
     def test_deepcopy_no_stdout(self, tmp_path):
         """
         Only BytesLoggers that log to stdout or stderr can be deepcopy-ed.
@@ -327,9 +343,27 @@ def test_passes_file(self):
 
         assert stderr is pl._file
 
-    def test_ignores_args(self):
+    def test_passes_name_from_args(self):
         """
-        BytesLogger doesn't take positional arguments.  If any are passed to
-        the factory, they are not passed to the logger.
+        The first positional argument is used as the logger name.
         """
-        BytesLoggerFactory()(1, 2, 3)
+        bl = BytesLoggerFactory()("my_logger")
+
+        assert "my_logger" == bl.name
+
+    def test_name_defaults_to_none(self):
+        """
+        If no positional arguments are passed to the factory, the logger
+        name defaults to None.
+        """
+        bl = BytesLoggerFactory()()
+
+        assert bl.name is None
+
+    def test_extra_args_ignored(self):
+        """
+        Positional arguments beyond the first are silently ignored.
+        """
+        bl = BytesLoggerFactory()("my_logger", 2, 3)
+
+        assert "my_logger" == bl.name
diff --git a/tests/test_stdlib.py b/tests/test_stdlib.py
index f54ae6b2..0488b4da 100644
--- a/tests/test_stdlib.py
+++ b/tests/test_stdlib.py
@@ -569,6 +569,29 @@ def test_logger_name_added_with_record(self, make_log_record):
 
         assert name == event_dict["logger"]
 
+    def test_logger_name_added_with_bytes_logger(self):
+        """
+        add_logger_name works with BytesLogger that has a name attribute.
+        """
+        from structlog import BytesLogger
+
+        name = "sample-name"
+        logger = BytesLogger(name=name)
+        event_dict = add_logger_name(logger, None, {})
+
+        assert name == event_dict["logger"]
+
+    def test_logger_name_none_with_unnamed_bytes_logger(self):
+        """
+        add_logger_name works with BytesLogger without a name, returning None.
+        """
+        from structlog import BytesLogger
+
+        logger = BytesLogger()
+        event_dict = add_logger_name(logger, None, {})
+
+        assert event_dict["logger"] is None
+
 
 def extra_dict() -> dict[str, Any]:
     """