diff --git a/homeassistant/components/random/binary_sensor.py b/homeassistant/components/random/binary_sensor.py
index 9d33ad52692..ae9a5886d59 100644
--- a/homeassistant/components/random/binary_sensor.py
+++ b/homeassistant/components/random/binary_sensor.py
@@ -59,10 +59,9 @@ class RandomBinarySensor(BinarySensorEntity):
 
     def __init__(self, config: Mapping[str, Any], entry_id: str | None = None) -> None:
         """Initialize the Random binary sensor."""
-        self._attr_name = config.get(CONF_NAME)
+        self._attr_name = config[CONF_NAME]
         self._attr_device_class = config.get(CONF_DEVICE_CLASS)
-        if entry_id:
-            self._attr_unique_id = entry_id
+        self._attr_unique_id = entry_id
 
     async def async_update(self) -> None:
         """Get new state and update the sensor's state."""
diff --git a/homeassistant/components/random/config_flow.py b/homeassistant/components/random/config_flow.py
index fcbd77916a9..00314169260 100644
--- a/homeassistant/components/random/config_flow.py
+++ b/homeassistant/components/random/config_flow.py
@@ -95,7 +95,7 @@ def _generate_schema(domain: str, flow_type: _FlowType) -> vol.Schema:
 
 
 async def choose_options_step(options: dict[str, Any]) -> str:
-    """Return next step_id for options flow according to template_type."""
+    """Return next step_id for options flow according to entity_type."""
     return cast(str, options["entity_type"])
 
 
@@ -122,7 +122,7 @@ def _validate_unit(options: dict[str, Any]) -> None:
 
 
 def validate_user_input(
-    template_type: str,
+    entity_type: str,
 ) -> Callable[
     [SchemaCommonFlowHandler, dict[str, Any]],
     Coroutine[Any, Any, dict[str, Any]],
@@ -136,10 +136,10 @@ def validate_user_input(
         _: SchemaCommonFlowHandler,
         user_input: dict[str, Any],
     ) -> dict[str, Any]:
-        """Add template type to user input."""
-        if template_type == Platform.SENSOR:
+        """Add entity type to user input."""
+        if entity_type == Platform.SENSOR:
             _validate_unit(user_input)
-        return {"entity_type": template_type} | user_input
+        return {"entity_type": entity_type} | user_input
 
     return _validate_user_input
 
diff --git a/homeassistant/components/random/sensor.py b/homeassistant/components/random/sensor.py
index 3c6e67c9918..aad4fcb851c 100644
--- a/homeassistant/components/random/sensor.py
+++ b/homeassistant/components/random/sensor.py
@@ -70,22 +70,22 @@ class RandomSensor(SensorEntity):
     """Representation of a Random number sensor."""
 
     _attr_translation_key = "random"
+    _unrecorded_attributes = frozenset({ATTR_MAXIMUM, ATTR_MINIMUM})
 
     def __init__(self, config: Mapping[str, Any], entry_id: str | None = None) -> None:
         """Initialize the Random sensor."""
-        self._attr_name = config.get(CONF_NAME)
-        self._minimum = config.get(CONF_MINIMUM, DEFAULT_MIN)
-        self._maximum = config.get(CONF_MAXIMUM, DEFAULT_MAX)
+        self._attr_name = config[CONF_NAME]
+        self._minimum = config[CONF_MINIMUM]
+        self._maximum = config[CONF_MAXIMUM]
         self._attr_native_unit_of_measurement = config.get(CONF_UNIT_OF_MEASUREMENT)
         self._attr_device_class = config.get(CONF_DEVICE_CLASS)
         self._attr_extra_state_attributes = {
             ATTR_MAXIMUM: self._maximum,
             ATTR_MINIMUM: self._minimum,
         }
-        if entry_id:
-            self._attr_unique_id = entry_id
+        self._attr_unique_id = entry_id
 
     async def async_update(self) -> None:
-        """Get a new number and updates the states."""
+        """Get a new number and update the state."""
 
         self._attr_native_value = randrange(self._minimum, self._maximum + 1)