diff --git a/homeassistant/components/motionmount/entity.py b/homeassistant/components/motionmount/entity.py
index c3f7c9c9358..8403af05491 100644
--- a/homeassistant/components/motionmount/entity.py
+++ b/homeassistant/components/motionmount/entity.py
@@ -1,5 +1,7 @@
 """Support for MotionMount sensors."""
 
+from typing import TYPE_CHECKING
+
 import motionmount
 
 from homeassistant.config_entries import ConfigEntry
@@ -42,12 +44,28 @@ class MotionMountEntity(Entity):
                 (dr.CONNECTION_NETWORK_MAC, mac)
             }
 
+    @property
+    def available(self) -> bool:
+        """Return True if the MotionMount is available (we're connected)."""
+        return self.mm.is_connected
+
+    def update_name(self) -> None:
+        """Update the name of the associated device."""
+        if TYPE_CHECKING:
+            assert self.device_entry
+        # Update the name in the device registry if needed
+        if self.device_entry.name != self.mm.name:
+            device_registry = dr.async_get(self.hass)
+            device_registry.async_update_device(self.device_entry.id, name=self.mm.name)
+
     async def async_added_to_hass(self) -> None:
         """Store register state change callback."""
         self.mm.add_listener(self.async_write_ha_state)
+        self.mm.add_listener(self.update_name)
         await super().async_added_to_hass()
 
     async def async_will_remove_from_hass(self) -> None:
         """Remove register state change callback."""
         self.mm.remove_listener(self.async_write_ha_state)
+        self.mm.remove_listener(self.update_name)
         await super().async_will_remove_from_hass()