Sorry to bump an older post. I ran into this issue myself.
For items that have an outdated name doing a forced Protect check in (a few times) via a policy was enough to get our device names to update. Mainly saw this on our newly enrolled devices running BigSur.
When an item is deleted from Pro it does not auto delete from Protect. To delete you could either manually delete from console or JAMF have provided some example scripts to clean up old computers. Be aware though that deleting from Protect does not remove the agent. API Scripts - Jamf Protect Documentation | Jamf