diff --git a/Lib/test/test_threading.py b/Lib/test/test_threading.py
index d02d3b3..2f0f3ae 100644
--- a/Lib/test/test_threading.py
+++ b/Lib/test/test_threading.py
@@ -20,6 +20,7 @@
 import signal
 import textwrap
 
+from unittest import mock
 from test import lock_tests
 from test import support
 
@@ -86,6 +87,33 @@
 
 class ThreadTests(BaseTestCase):
 
+    @cpython_only
+    def test_name(self):
+        def func(): pass
+
+        thread = threading.Thread(name="myname1")
+        self.assertEqual(thread.name, "myname1")
+
+        # Convert int name to str
+        thread = threading.Thread(name=123)
+        self.assertEqual(thread.name, "123")
+
+        # target name is ignored if name is specified
+        thread = threading.Thread(target=func, name="myname2")
+        self.assertEqual(thread.name, "myname2")
+
+        with mock.patch.object(threading, '_counter', return_value=2):
+            thread = threading.Thread(name="")
+            self.assertEqual(thread.name, "Thread-2")
+
+        with mock.patch.object(threading, '_counter', return_value=3):
+            thread = threading.Thread()
+            self.assertEqual(thread.name, "Thread-3")
+
+        with mock.patch.object(threading, '_counter', return_value=5):
+            thread = threading.Thread(target=func)
+            self.assertEqual(thread.name, "Thread-5 (func)")
+
     # Create a bunch of threads, let each do some work, wait until all are
     # done.
     def test_various_ops(self):
@@ -531,7 +559,7 @@
             import os, threading, sys
             from test import support
 
-            def f():
+            def func():
                 pid = os.fork()
                 if pid == 0:
                     main = threading.main_thread()
@@ -544,14 +572,14 @@
                 else:
                     support.wait_process(pid, exitcode=0)
 
-            th = threading.Thread(target=f)
+            th = threading.Thread(target=func)
             th.start()
             th.join()
         """
         _, out, err = assert_python_ok("-c", code)
         data = out.decode().replace('\r', '')
         self.assertEqual(err, b"")
-        self.assertEqual(data, "Thread-1\nTrue\nTrue\n")
+        self.assertEqual(data, "Thread-1 (func)\nTrue\nTrue\n")
 
     def test_main_thread_during_shutdown(self):
         # bpo-31516: current_thread() should still point to the main thread
diff --git a/Lib/threading.py b/Lib/threading.py
index ab29db7..06c77f7 100644
--- a/Lib/threading.py
+++ b/Lib/threading.py
@@ -745,10 +745,9 @@
 
 
 # Helper to generate new thread names
-_counter = _count().__next__
-_counter() # Consume 0 so first non-main thread has id 1.
-def _newname(template="Thread-%d"):
-    return template % _counter()
+_counter = _count(1).__next__
+def _newname(name_template):
+    return name_template % _counter()
 
 # Active thread administration
 _active_limbo_lock = _allocate_lock()
@@ -800,8 +799,19 @@
         assert group is None, "group argument must be None for now"
         if kwargs is None:
             kwargs = {}
+        if name:
+            name = str(name)
+        else:
+            name = _newname("Thread-%d")
+            if target is not None:
+                try:
+                    target_name = target.__name__
+                    name += f" ({target_name})"
+                except AttributeError:
+                    pass
+
         self._target = target
-        self._name = str(name or _newname())
+        self._name = name
         self._args = args
         self._kwargs = kwargs
         if daemon is not None: