diff --git a/src/easyscience/global_object/map.py b/src/easyscience/global_object/map.py
index 53a3aac4..7edacba1 100644
--- a/src/easyscience/global_object/map.py
+++ b/src/easyscience/global_object/map.py
@@ -126,7 +126,19 @@ def change_type(self, obj, new_type: str):
     def add_vertex(self, obj: object, obj_type: str = None):
         name = obj.unique_name
         if name in self._store.keys():
-            raise ValueError(f'Object name {name} already exists in the graph.')
+            # modify the name to make it unique:
+            #  add "_1" or increment the number if already exists
+            suffix = 1
+            base_name = name
+            new_name = base_name + '_' + str(suffix)
+            while new_name in self._store.keys():
+                suffix += 1
+                new_name = base_name + '_' + str(suffix)
+            # Update the object's unique_name directly to avoid recursive add_vertex call
+            obj._unique_name = new_name  # Direct assignment to avoid setter
+            name = new_name
+            # too much overhead in logging
+            # print(f"Warning: Object name already exists. Changed to unique name '{name}'")
         self._store[name] = obj
         self.__type_dict[name] = _EntryList()  # Add objects type to the list of types
         self.__type_dict[name].finalizer = weakref.finalize(self._store[name], self.prune, name)
diff --git a/tests/unit_tests/global_object/test_map.py b/tests/unit_tests/global_object/test_map.py
index df344aed..fb64835a 100644
--- a/tests/unit_tests/global_object/test_map.py
+++ b/tests/unit_tests/global_object/test_map.py
@@ -58,12 +58,36 @@ def test_get_item_by_key(self, clear, base_object, parameter_object):
         assert global_object.map.get_item_by_key(parameter_object.unique_name) == parameter_object
 
     @pytest.mark.parametrize("cls, kwargs", [(ObjBase, {}), (Parameter, {"value": 2.0})])
-    def test_identical_unique_names_exception(self, clear, cls, kwargs):
+    def test_identical_unique_names_auto_rename(self, clear, cls, kwargs):
         # When
         test_obj = cls(name="test", unique_name="test", **kwargs)
-        # Then Expect
-        with pytest.raises(ValueError):
-            test_obj2 = cls(name="test2", unique_name="test", **kwargs)
+        original_unique_name = test_obj.unique_name
+        # Then
+        test_obj2 = cls(name="test2", unique_name="test", **kwargs)
+        # Expect - the second object should be automatically renamed
+        assert test_obj.unique_name == original_unique_name  # First object keeps original name
+        assert test_obj2.unique_name == "test_1"  # Second object gets suffix
+        assert test_obj.unique_name != test_obj2.unique_name  # Names are different
+        # Both objects should be in the map with their respective names
+        assert global_object.map.get_item_by_key(test_obj.unique_name) == test_obj
+        assert global_object.map.get_item_by_key(test_obj2.unique_name) == test_obj2
+
+    def test_multiple_identical_unique_names_increment(self, clear):
+        # When - Create multiple objects with the same initial unique name
+        obj1 = ObjBase(name="test1", unique_name="duplicate")
+        obj2 = ObjBase(name="test2", unique_name="duplicate")
+        obj3 = ObjBase(name="test3", unique_name="duplicate")
+
+        # Expect - Each should get a unique incremented name
+        assert obj1.unique_name == "duplicate"  # First keeps original
+        assert obj2.unique_name == "duplicate_1"  # Second gets _1
+        assert obj3.unique_name == "duplicate_2"  # Third gets _2
+
+        # All should be accessible in the map
+        assert global_object.map.get_item_by_key("duplicate") == obj1
+        assert global_object.map.get_item_by_key("duplicate_1") == obj2
+        assert global_object.map.get_item_by_key("duplicate_2") == obj3
+        assert len(global_object.map._store) == 3
 
     def test_unique_name_change_still_in_map(self, clear, base_object, parameter_object):
         # When