Change naming of MQTT entities to correspond with HA guidelines (#95159)

* Set has_entity_name if device_name is set

* revert unneeded formatting change

* Add image platform

* Follow up comment

* Don't set `has_entity_name` without device name

* Only set has_entity_name if a valid name is set

* Follow device_class name and add tests

* Follow up comments add extra tests

* Move to helper - Log a warning

* fix test

* Allow to assign None as name explictly

* Refactor

* Log info messages when device name is not set

* Revert scene schema change - no device link

* Always set has_entity_name with device mapping

* Always set `_attr_has_entity_name`

* Cleanup

tests/components/mqtt/test_sensor.py

@@ -53,6 +53,7 @@ from .test_common import (
     help_test_entity_disabled_by_default,
     help_test_entity_id_update_discovery_update,
     help_test_entity_id_update_subscriptions,
+    help_test_entity_name,
     help_test_reload_with_config,
     help_test_reloadable,
     help_test_setting_attribute_via_mqtt_json_message,
@@ -1409,3 +1410,21 @@ async def test_unload_entry(
     await help_test_unload_config_entry_with_platform(
         hass, mqtt_mock_entry, domain, config
     )
+
+
+@pytest.mark.parametrize(
+    ("expected_friendly_name", "device_class"),
+    [("test", None), ("Humidity", "humidity"), ("Temperature", "temperature")],
+)
+async def test_entity_name(
+    hass: HomeAssistant,
+    mqtt_mock_entry: MqttMockHAClientGenerator,
+    expected_friendly_name: str | None,
+    device_class: str | None,
+) -> None:
+    """Test the entity name setup."""
+    domain = sensor.DOMAIN
+    config = DEFAULT_CONFIG
+    await help_test_entity_name(
+        hass, mqtt_mock_entry, domain, config, expected_friendly_name, device_class
+    )