diff --git a/_pytest/python.py b/_pytest/python.py
index 650171a9e9c..57ebcfbb32e 100644
--- a/_pytest/python.py
+++ b/_pytest/python.py
@@ -933,7 +933,7 @@ def _idval(val, argname, idx, idfn, config=None):
         return ascii_escaped(val.pattern)
     elif enum is not None and isinstance(val, enum.Enum):
         return str(val)
-    elif isclass(val) and hasattr(val, '__name__'):
+    elif (isclass(val) or isfunction(val)) and hasattr(val, '__name__'):
         return val.__name__
     return str(argname) + str(idx)
 
diff --git a/changelog/2976.trivial b/changelog/2976.trivial
new file mode 100644
index 00000000000..5f767dd2740
--- /dev/null
+++ b/changelog/2976.trivial
@@ -0,0 +1 @@
+Change parametrized automatic test id generation to use the ``__name__`` attribute of functions instead of the fallback argument name plus counter.
diff --git a/testing/python/metafunc.py b/testing/python/metafunc.py
index 2ffb7bb5da2..0ed9f56bfee 100644
--- a/testing/python/metafunc.py
+++ b/testing/python/metafunc.py
@@ -235,6 +235,25 @@ def test_bytes_idval(self):
         for val, expected in values:
             assert _idval(val, 'a', 6, None) == expected
 
+    def test_class_or_function_idval(self):
+        """unittest for the expected behavior to obtain ids for parametrized
+        values that are classes or functions: their __name__.
+        """
+        from _pytest.python import _idval
+
+        class TestClass:
+            pass
+
+        def test_function():
+            pass
+
+        values = [
+            (TestClass, "TestClass"),
+            (test_function, "test_function"),
+        ]
+        for val, expected in values:
+            assert _idval(val, 'a', 6, None) == expected
+
     @pytest.mark.issue250
     def test_idmaker_autoname(self):
         from _pytest.python import idmaker