Since one of my player schould be named „Küche“ I had the same problem.
The name in the “Settings/Reboot” menu seems to be linked with the hostname… no option 😉
So thanks to FareakyGnome for the tip with the playername.txt
Like Maximilian wrote: the most simple solution: just set the name in the audioplayer extended options:
-n Küche added to the squeezelite starting parameters works always (not just with multisqueeze)!