My daughter goes through phones like candy… breaks them. Each time the phone creates new sensors and device trackers. How in the heck do I get rid of all of the old ones? It is a real pain finding the live ones, renaming the last one and renaming the new one.
If you want everything to have the same name, always when you switch devices, then yes remove before logging into the new device. Then set the name when you login.
If you want a new name for the device then set that when you login and just remove the old device.