diff --git a/mira/metamodel/ops.py b/mira/metamodel/ops.py
index ec059f2c..3bae168d 100644
--- a/mira/metamodel/ops.py
+++ b/mira/metamodel/ops.py
@@ -229,14 +229,12 @@ def stratify(
                     # We now apply the stratum assigned to each controller in this particular
                     # tuple to the controller
                     for controller, c_stratum in zip(stratified_controllers, c_strata_tuple):
+                        stratified_template.name += f"_{c_stratum}"
                         controller.with_context(do_rename=modify_names, inplace=True,
                                                 **{key: c_stratum})
                         template_strata.append(c_stratum if param_renaming_uses_strata_names
                                                else stratum_index_map[c_stratum])
 
-                    tname = stratified_template.name if stratified_template.name \
-                        else 't' + '_'.join(template_strata)
-                    stratified_template.name = tname
                     # Wew can now rewrite the rate law for this stratified template,
                     # then append the new template
                     param_mappings = rewrite_rate_law(template_model=template_model,
diff --git a/tests/test_ops.py b/tests/test_ops.py
index fe5bf8f5..79ee8e86 100644
--- a/tests/test_ops.py
+++ b/tests/test_ops.py
@@ -42,6 +42,7 @@ def test_stratify_full(self):
         )
 
         expected_0 = ControlledConversion(
+            name="t_unvaccinated_unvaccinated",
             subject=susceptible.with_context(vaccination_status="unvaccinated",
                                              do_rename=True),
             outcome=infected.with_context(vaccination_status="unvaccinated",
@@ -54,6 +55,7 @@ def test_stratify_full(self):
             )
         )
         expected_1 = ControlledConversion(
+            name="t_unvaccinated_vaccinated",
             subject=susceptible.with_context(vaccination_status="unvaccinated",
                                              do_rename=True),
             outcome=infected.with_context(vaccination_status="unvaccinated",
@@ -66,6 +68,7 @@ def test_stratify_full(self):
             )
         )
         expected_2 = ControlledConversion(
+            name="t_vaccinated_unvaccinated",
             subject=susceptible.with_context(vaccination_status="vaccinated",
                                              do_rename=True),
             outcome=infected.with_context(vaccination_status="vaccinated",
@@ -78,6 +81,7 @@ def test_stratify_full(self):
             )
         )
         expected_3 = ControlledConversion(
+            name="t_vaccinated_vaccinated",
             subject=susceptible.with_context(vaccination_status="vaccinated",
                                              do_rename=True),
             outcome=infected.with_context(vaccination_status="vaccinated",