diff --git a/Doc/whatsnew/3.16.rst b/Doc/whatsnew/3.16.rst
index 3d3125ad17b126b..3d514b7bd316404 100644
--- a/Doc/whatsnew/3.16.rst
+++ b/Doc/whatsnew/3.16.rst
@@ -1045,6 +1045,16 @@ that may require changes to your code.
   raises :exc:`io.UnsupportedOperation` unless buffering is disabled.
   (Contributed by An Long in :gh:`86768`.)
 
+* :mod:`gzip` and :mod:`tarfile` now derive the ``FNAME`` field of the gzip
+  header from the file name like :program:`gunzip` does: the suffix is matched
+  ignoring case, and ``.tgz`` is replaced with ``.tar`` instead of being left
+  in place.  For example, an archive created as :file:`spam.tgz` now records
+  ``spam.tar`` rather than ``spam.tgz``, and :file:`spam.GZ` records ``spam``
+  rather than ``spam.GZ``.  Code comparing generated files byte for byte may
+  need to be updated.  ``python -m gzip -d`` accepts the same names, where it
+  previously refused anything not ending in a lowercase ``.gz``.
+  (Contributed by Dmitry Voropaev in :gh:`88661`.)
+
 
 Build changes
 =============
diff --git a/Lib/gzip.py b/Lib/gzip.py
index 247efc01527bb14..4853ace32167aa7 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -145,6 +145,25 @@ def writable(self):
         return True
 
 
+def _gunzip_name(name):
+    """The name :program:`gunzip` would decompress *name* to, or ``None``.
+
+    The suffix is matched ignoring case, and ``.tgz`` becomes ``.tar`` rather
+    than being stripped.  ``.taz`` is not handled: it means a ``.tar.Z``, and
+    this module does not do :program:`compress`.  Accepts and returns either
+    :class:`str` or :class:`bytes`.
+    """
+    if isinstance(name, bytes):
+        gz, tgz, tar = b'.gz', b'.tgz', b'.tar'
+    else:
+        gz, tgz, tar = '.gz', '.tgz', '.tar'
+    if name[-3:].lower() == gz:
+        return name[:-3]
+    if name[-4:].lower() == tgz:
+        return name[:-4] + tar
+    return None
+
+
 class GzipFile(_streams.BaseStream):
     """The GzipFile class simulates most of the methods of a file object with
     the exception of the truncate() method.
@@ -288,8 +307,9 @@ def _write_gzip_header(self, compresslevel):
             fname = os.path.basename(self.name)
             if not isinstance(fname, bytes):
                 fname = fname.encode('latin-1')
-            if fname.endswith(b'.gz'):
-                fname = fname[:-3]
+            stripped = _gunzip_name(fname)
+            if stripped is not None:
+                fname = stripped
         except UnicodeEncodeError:
             fname = b''
         flags = 0
@@ -729,10 +749,11 @@ def main():
                 f = GzipFile(filename="", mode="rb", fileobj=sys.stdin.buffer)
                 g = sys.stdout.buffer
             else:
-                if arg[-3:] != ".gz":
-                    sys.exit(f"filename doesn't end in .gz: {arg!r}")
+                out = _gunzip_name(arg)
+                if out is None:
+                    sys.exit(f"filename doesn't end in .gz or .tgz: {arg!r}")
                 f = open(arg, "rb")
-                g = builtins.open(arg[:-3], "wb")
+                g = builtins.open(out, "wb")
         else:
             if arg == "-":
                 f = sys.stdin.buffer
diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index a4f9ce3311f6dad..f908d23cc6d9ab9 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -456,8 +456,13 @@ def _init_write_gz(self, compresslevel, mtime):
             mtime = int(time.time())
         timestamp = struct.pack("<L", mtime)
         self.__write(b"\037\213\010\010" + timestamp + b"\002\377")
-        if self.name.endswith(".gz"):
+        # Like gunzip, match the suffix ignoring case, and turn ".tgz" into
+        # ".tar" instead of just stripping it.  (gzip._gunzip_name does the
+        # same, but importing gzip here would pull it into the w|gz path.)
+        if self.name[-3:].lower() == ".gz":
             self.name = self.name[:-3]
+        elif self.name[-4:].lower() == ".tgz":
+            self.name = self.name[:-4] + ".tar"
         # Honor "directory components removed" from RFC1952
         self.name = os.path.basename(self.name)
         # RFC1952 says we must use ISO-8859-1 for the FNAME field.
diff --git a/Lib/test/test_gzip.py b/Lib/test/test_gzip.py
index 8bc8e507683cb50..1c4b06f388de8bc 100644
--- a/Lib/test/test_gzip.py
+++ b/Lib/test/test_gzip.py
@@ -437,6 +437,39 @@ def test_metadata_ascii_name(self):
         self.filename = os_helper.TESTFN_ASCII
         self.test_metadata()
 
+    def test_metadata_name_suffix(self):
+        # gh-88661: the FNAME field holds the name that the file is expected
+        # to have after decompression.  Like gunzip, the suffix is matched
+        # ignoring case, and ".tgz" is turned into ".tar".
+        base = os_helper.TESTFN_ASCII
+        # Only the suffix is matched ignoring case; the rest of the name
+        # keeps the case it was given, the way make_ofname() does in gunzip.
+        upper = base.upper()
+        for filename, expected in ((base, base),
+                                   (base + '.gz', base),
+                                   (base + '.GZ', base),
+                                   (base + '.gZ', base),
+                                   (base + '.tgz', base + '.tar'),
+                                   (base + '.TGZ', base + '.tar'),
+                                   (base + '.tGz', base + '.tar'),
+                                   (base + '.tar', base + '.tar'),
+                                   # .taz means .tar.Z, which this module cannot read.
+                                   (base + '.taz', base + '.taz'),
+                                   (base + '.tgz.gz', base + '.tgz'),
+                                   (upper + '.GZ', upper),
+                                   (upper + '.TGZ', upper + '.tar')):
+            with self.subTest(filename=filename):
+                try:
+                    with gzip.GzipFile(filename, 'w') as f:
+                        f.write(data1)
+                    with open(filename, 'rb') as f:
+                        header = f.read(1024)
+                    self.assertEqual(header[3], 8)  # only the FNAME flag
+                    fname = header[10:header.index(b'\0', 10)]
+                    self.assertEqual(fname.decode('latin-1'), expected)
+                finally:
+                    os_helper.unlink(filename)
+
     def test_compresslevel_metadata(self):
         # see RFC 1952: http://www.faqs.org/rfcs/rfc1952.html
         # specifically, discussion of XFL in section 2.3.1
@@ -1153,10 +1186,37 @@ def test_decompress_infile_outfile(self):
         self.assertEqual(err, b'')
 
     def test_decompress_infile_outfile_error(self):
-        rc, out, err = assert_python_failure('-m', 'gzip', '-d', 'thisisatest.out')
-        self.assertEqual(b"filename doesn't end in .gz: 'thisisatest.out'", err.strip())
-        self.assertEqual(rc, 1)
-        self.assertEqual(out, b'')
+        # ".taz" is a ".tar.Z", which this module cannot read, so it is
+        # rejected along with names that carry no gzip suffix at all.
+        for name in ('thisisatest.out', 'thisisatest.taz'):
+            with self.subTest(name=name):
+                rc, out, err = assert_python_failure('-m', 'gzip', '-d', name)
+                self.assertEqual(
+                    f"filename doesn't end in .gz or .tgz: {name!r}".encode(),
+                    err.strip())
+                self.assertEqual(rc, 1)
+                self.assertEqual(out, b'')
+
+    @create_and_remove_directory(TEMPDIR)
+    def test_decompress_suffix_like_gunzip(self):
+        # gh-88661: the command line accepts the names gunzip accepts, and
+        # writes the name gunzip would write.
+        # Distinct stems: the names differ only in case on some platforms,
+        # and a case-insensitive filesystem would have them collide.
+        for name, expected in (('lower.tgz', 'lower.tar'),
+                               ('upper.TGZ', 'upper.tar'),
+                               ('caps.GZ', 'caps')):
+            with self.subTest(name=name):
+                path = os.path.join(TEMPDIR, name)
+                with gzip.open(path, mode='wb') as fp:
+                    fp.write(self.data)
+
+                rc, out, err = assert_python_ok('-m', 'gzip', '-d', path)
+                self.assertEqual(rc, 0)
+                self.assertEqual(err, b'')
+
+                with open(os.path.join(TEMPDIR, expected), 'rb') as gunziped:
+                    self.assertEqual(gunziped.read(), self.data)
 
     @requires_subprocess()
     @create_and_remove_directory(TEMPDIR)
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 55f052d0504d67b..3f18dff88276248 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1967,7 +1967,42 @@ def test_missing_fileobj(self):
                 tar.addfile(tarinfo)
 
 
-class GzipWriteTest(GzipTest, WriteTest):
+class GzipFnameTestBase:
+    # gh-88661: the FNAME field of the gzip header holds the name that the
+    # archive is expected to have after decompression.  Like gunzip, the
+    # suffix is matched ignoring case, and ".tgz" becomes ".tar".
+
+    def gzip_header_fname(self, path):
+        with open(path, "rb") as fobj:
+            header = fobj.read(1024)
+        self.assertEqual(header[:2], b"\037\213")  # gzip magic number
+        self.assertEqual(header[3], 8)  # only the FNAME flag
+        return header[10:header.index(b"\0", 10)].decode("latin-1")
+
+    def test_fname(self):
+        # Only the suffix is matched ignoring case; the rest of the name
+        # keeps the case it was given, the way make_ofname() does in gunzip.
+        for name, expected in (("tmp.tar.gz", "tmp.tar"),
+                               ("tmp.TAR.GZ", "tmp.TAR"),
+                               ("tmp.tgz", "tmp.tar"),
+                               ("tmp.TGZ", "tmp.tar"),
+                               ("tmp.tGz", "tmp.tar"),
+                               # .taz means .tar.Z, not gzip.
+                               ("tmp.taz", "tmp.taz"),
+                               ("tmp.TAZ", "tmp.TAZ"),
+                               ("TMP.TGZ", "TMP.tar"),
+                               ("TMP.TAZ", "TMP.TAZ"),
+                               ("tmp.tar", "tmp.tar")):
+            with self.subTest(name=name):
+                path = os.path.join(TEMPDIR, name)
+                try:
+                    tarfile.open(path, self.mode).close()
+                    self.assertEqual(self.gzip_header_fname(path), expected)
+                finally:
+                    os_helper.unlink(path)
+
+
+class GzipWriteTest(GzipTest, GzipFnameTestBase, WriteTest):
     pass
 
 
@@ -2034,7 +2069,7 @@ def test_pathlike_name(self):
                 os_helper.unlink(tmpname)
 
 
-class GzipStreamWriteTest(GzipTest, StreamWriteTest):
+class GzipStreamWriteTest(GzipTest, GzipFnameTestBase, StreamWriteTest):
     def test_source_directory_not_leaked(self):
         """
         Ensure the source directory is not included in the tar header
diff --git a/Misc/NEWS.d/next/Library/2026-09-24-18-23-43.gh-issue-88661.vOpGJy.rst b/Misc/NEWS.d/next/Library/2026-09-24-18-23-43.gh-issue-88661.vOpGJy.rst
new file mode 100644
index 000000000000000..22b3ffcc5356a20
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-09-24-18-23-43.gh-issue-88661.vOpGJy.rst
@@ -0,0 +1,6 @@
+When writing a gzip header, :mod:`gzip` and :mod:`tarfile` now derive the
+``FNAME`` field from the file name like :program:`gunzip` does: the suffix is
+matched ignoring case, and ``.tgz`` is replaced with ``.tar`` instead of being
+left in place.  Previously an archive created as :file:`spam.tgz` recorded
+``spam.tgz`` as the name to decompress to.  ``python -m gzip -d`` now accepts
+the same names, so :file:`spam.tgz` and :file:`spam.GZ` are no longer refused.