diff --git a/Lib/bz2.py b/Lib/bz2.py
index a2c588e748..4e9d1bcbdc 100644
--- a/Lib/bz2.py
+++ b/Lib/bz2.py
@@ -79,10 +79,12 @@ def __init__(self, filename, mode="r", *, compresslevel=9):
 
         if isinstance(filename, (str, bytes, os.PathLike)):
             self._fp = _builtin_open(filename, mode)
+            self.filename = filename
             self._closefp = True
             self._mode = mode_code
         elif hasattr(filename, "read") or hasattr(filename, "write"):
             self._fp = filename
+            self.filename = self._fp.name
             self._mode = mode_code
         else:
             raise TypeError("filename must be a str, bytes, file or PathLike object")
@@ -263,6 +265,9 @@ def tell(self):
             return self._buffer.tell()
         return self._pos
 
+    def name(self):
+        return self.filename
+
 
 def open(filename, mode="rb", compresslevel=9,
          encoding=None, errors=None, newline=None):
diff --git a/Lib/test/test_bz2.py b/Lib/test/test_bz2.py
index efed3a859b..2d50150f4e 100644
--- a/Lib/test/test_bz2.py
+++ b/Lib/test/test_bz2.py
@@ -105,6 +105,11 @@ def testBadArgs(self):
         # compresslevel is keyword-only
         self.assertRaises(TypeError, BZ2File, os.devnull, "r", 3)
 
+    def testNameExists(self):
+        with self.createTempFile() as fin:
+            with BZ2File(fin) as bz2f:
+                self.assertTrue((bz2f.name is not None) and (bz2f.name == self.filename))
+
     def testRead(self):
         self.createTempFile()
         with BZ2File(self.filename) as bz2f: