diff --git a/homeassistant/components/script/__init__.py b/homeassistant/components/script/__init__.py
index 2a950c749ac..660e7233b33 100644
--- a/homeassistant/components/script/__init__.py
+++ b/homeassistant/components/script/__init__.py
@@ -319,6 +319,10 @@ class ScriptEntity(ToggleEntity, RestoreEntity):
         self.description = cfg[CONF_DESCRIPTION]
         self.fields = cfg[CONF_FIELDS]
 
+        # The object ID of scripts need / are unique already
+        # they cannot be changed from the UI after creating
+        self._attr_unique_id = object_id
+
         self.entity_id = ENTITY_ID_FORMAT.format(object_id)
         self.script = Script(
             hass,
diff --git a/tests/components/script/test_init.py b/tests/components/script/test_init.py
index 3bd179286a9..680293b57d7 100644
--- a/tests/components/script/test_init.py
+++ b/tests/components/script/test_init.py
@@ -25,7 +25,7 @@ from homeassistant.core import (
     split_entity_id,
 )
 from homeassistant.exceptions import ServiceNotFound
-from homeassistant.helpers import template
+from homeassistant.helpers import entity_registry as er, template
 from homeassistant.helpers.event import async_track_state_change
 from homeassistant.helpers.script import (
     SCRIPT_MODE_CHOICES,
@@ -205,7 +205,8 @@ async def test_reload_service(hass, running):
         await hass.async_block_till_done()
 
     if running != "same":
-        assert hass.states.get(ENTITY_ID) is None
+        state = hass.states.get(ENTITY_ID)
+        assert state.attributes["restored"] is True
         assert not hass.services.has_service(script.DOMAIN, "test")
 
         assert hass.states.get("script.test2") is not None
@@ -482,6 +483,11 @@ async def test_config_basic(hass):
     assert test_script.name == "Script Name"
     assert test_script.attributes["icon"] == "mdi:party"
 
+    registry = er.async_get(hass)
+    entry = registry.async_get("script.test_script")
+    assert entry
+    assert entry.unique_id == "test_script"
+
 
 async def test_config_multiple_domains(hass):
     """Test splitting configuration over multiple domains."""