So those videos are not of you trying to rename them? The videos show the devices being renamed successfully.
What exactly is happening when you try to rename them?
they are my videos! I am renaming my magic mouse and my keyboard and it looked good when I pressed rename but when I go back in the system settings and go back to the bluetooth preferences just to look for the name again if it worked it still shows me the the old name again!
Did you find a solution to this? I am having the exact same problem, get to the rename screen, click done & it appears that it's updated with the new name but when I go back into it - the old name is still there. I have Catalina, no access to anything with Mojave to test either