diff --git a/Python/ceval.c b/Python/ceval.c
index 53b596b..326930b 100644
--- a/Python/ceval.c
+++ b/Python/ceval.c
@@ -6319,6 +6319,20 @@ format_exc_check_arg(PyThreadState *tstate, PyObject *exc,
         return;
 
     _PyErr_Format(tstate, exc, format_str, obj_str);
+
+    if (exc == PyExc_NameError) {
+        // Include the name in the NameError exceptions to offer suggestions later.
+        _Py_IDENTIFIER(name);
+        PyObject *type, *value, *traceback;
+        PyErr_Fetch(&type, &value, &traceback);
+        PyErr_NormalizeException(&type, &value, &traceback);
+        if (PyErr_GivenExceptionMatches(value, PyExc_NameError)) {
+            // We do not care if this fails because we are going to restore the
+            // NameError anyway.
+            (void)_PyObject_SetAttrId(value, &PyId_name, obj);
+        }
+        PyErr_Restore(type, value, traceback);
+    }
 }
 
 static void