@CorinaM,

To have the devices maintain their name after they disconnect from the network, you would need to either set up IP reservations or add the devices to a parental control profile so that the feature will instead MAC addresses to keep their custom names.

If you have phones that are not appearing correctly, it is possible that the private addressing feature is enabled for your home network on your phone. With this phone setting enabled, there is no way for the router to identify the device as a known client, as the MAC address is randomized each time your phone connects to the network