diff --git a/control/iosys.py b/control/iosys.py
index 2881c5d64..4d697cf3d 100644
--- a/control/iosys.py
+++ b/control/iosys.py
@@ -2405,7 +2405,10 @@ def ss(*args, **kwargs):
 
             # Create a state space system from an LTI system
             sys = LinearIOSystem(
-                _convert_to_statespace(sys, use_prefix_suffix=True), **kwargs)
+                _convert_to_statespace(
+                    sys,
+                    use_prefix_suffix=not sys._generic_name_check()),
+                **kwargs)
 
         else:
             raise TypeError("ss(sys): sys must be a StateSpace or "
diff --git a/control/statesp.py b/control/statesp.py
index d3d1ab1d0..d1fa16b63 100644
--- a/control/statesp.py
+++ b/control/statesp.py
@@ -1914,8 +1914,11 @@ def tf2ss(*args, **kwargs):
         if not isinstance(sys, TransferFunction):
             raise TypeError("tf2ss(sys): sys must be a TransferFunction "
                             "object.")
-        return StateSpace(_convert_to_statespace(sys, use_prefix_suffix=True),
-                          **kwargs)
+        return StateSpace(
+            _convert_to_statespace(
+                sys,
+                use_prefix_suffix=not sys._generic_name_check()),
+            **kwargs)
     else:
         raise ValueError("Needs 1 or 2 arguments; received %i." % len(args))
 
diff --git a/control/tests/namedio_test.py b/control/tests/namedio_test.py
index cf30b94aa..80b085b5a 100644
--- a/control/tests/namedio_test.py
+++ b/control/tests/namedio_test.py
@@ -135,6 +135,8 @@ def test_io_naming(fun, args, kwargs):
         sys_r.set_states(state_labels)
         assert sys_r.state_labels == state_labels
 
+    sys_r.name = 'sys'          # make sure name is non-generic
+
     #
     # Set names using keywords and make sure they stick
     #
diff --git a/control/tests/xferfcn_test.py b/control/tests/xferfcn_test.py
index 7d561e770..078ad4453 100644
--- a/control/tests/xferfcn_test.py
+++ b/control/tests/xferfcn_test.py
@@ -1254,7 +1254,7 @@ def test_zpk(zeros, poles, gain, args, kwargs):
 ])
 def test_copy_names(create, args, kwargs, convert):
     # Convert a system with no renaming
-    sys = create(*args, **kwargs)
+    sys = create(*args, **kwargs, name='sys')
     cpy = convert(sys)
 
     assert cpy.input_labels == sys.input_labels
diff --git a/control/xferfcn.py b/control/xferfcn.py
index 60a40eca0..7664c16ac 100644
--- a/control/xferfcn.py
+++ b/control/xferfcn.py
@@ -1813,7 +1813,8 @@ def ss2tf(*args, **kwargs):
             if not kwargs.get('outputs'):
                 kwargs['outputs'] = sys.output_labels
             return TransferFunction(
-                _convert_to_transfer_function(sys, use_prefix_suffix=True),
+                _convert_to_transfer_function(
+                    sys, use_prefix_suffix=not sys._generic_name_check()),
                 **kwargs)
         else:
             raise TypeError(