diff --git a/datalad/support/exceptions.py b/datalad/support/exceptions.py
index 48a86ce7c2..159507275f 100644
--- a/datalad/support/exceptions.py
+++ b/datalad/support/exceptions.py
@@ -11,6 +11,7 @@
 
 import logging
 import re
+import sys
 import traceback
 from os import linesep
 from pathlib import Path
@@ -112,15 +113,26 @@ def message(self):
         """
         return str(self.tb)
 
-    @property
-    def name(self):
-        """Returns the class name of the original exception
+    if sys.version_info < (3, 13):
+        @property
+        def name(self):
+            """Returns the class name of the original exception
 
-        Returns
-        -------
-        str
-        """
-        return self.tb.exc_type.__qualname__
+            Returns
+            -------
+            str
+            """
+            return self.tb.exc_type.__qualname__
+    else:
+        @property
+        def name(self):
+            """Returns the class name of the original exception
+
+            Returns
+            -------
+            str
+            """
+            return self.tb.exc_type_str
 
     def __str__(self):
         return self.format_short()
@@ -210,7 +222,8 @@ class name of the exception, with the aim to generate a simple and
     messages.
     """
     s = str(e) or \
-        (e.exc_type.__name__ if isinstance(e, traceback.TracebackException)
+        ((e.exc_type.__name__ if sys.version_info < (3, 13) else e.exc_type_str)
+         if isinstance(e, traceback.TracebackException)
          else e.__class__.__name__)
     exc_cause = getattr(e, '__cause__', None)
     if exc_cause:
diff --git a/datalad/support/tests/test_captured_exception.py b/datalad/support/tests/test_captured_exception.py
index dd5a9db143..2621194410 100644
--- a/datalad/support/tests/test_captured_exception.py
+++ b/datalad/support/tests/test_captured_exception.py
@@ -1,3 +1,4 @@
+import sys
 from unittest.mock import patch
 
 from datalad import cfg
@@ -72,15 +73,16 @@ def f2():
     assert_equal(full_display[0], "Traceback (most recent call last):")
     # points in f and f2 for first exception with two lines each
     # (where is the line and what reads the line):
-    assert_true(full_display[1].lstrip().startswith("File"))
-    assert_equal(full_display[2].strip(), "f2()")
-    assert_true(full_display[3].lstrip().startswith("File"))
-    assert_equal(full_display[4].strip(), "raise Exception(\"my bad again\")")
-    assert_equal(full_display[5].strip(), "Exception: my bad again")
-    assert_equal(full_display[7].strip(), "The above exception was the direct cause of the following exception:")
-    assert_equal(full_display[9], "Traceback (most recent call last):")
+    assert full_display[1].lstrip().startswith("File")
+    assert full_display[2].strip() == "f2()"
+    inc = int(sys.version_info >= (3, 13))
+    assert full_display[3 + inc].lstrip().startswith("File")
+    assert full_display[4 + inc].strip() == "raise Exception(\"my bad again\")"
+    assert full_display[5 + inc].strip() == "Exception: my bad again"
+    assert full_display[7 + inc].strip() == "The above exception was the direct cause of the following exception:"
+    assert full_display[9 + inc] == "Traceback (most recent call last):"
     # ...
-    assert_equal(full_display[-1].strip(), "RuntimeError: new message")
+    assert full_display[-1].strip() == "RuntimeError: new message"
 
     # CapturedException.__repr__:
     assert_re_in(r".*test_captured_exception.py:f2:[0-9]+\]$",