Edit Apple Device name
How do I edit the names of my Apple TV's which appear on my phone when I "airplay" ? We have moved around the Apple TVs and the room names are now different
Apple TV 4, tvOS 13
See the following from Manage AirPlay settings on your Apple TV - Apple Support
Give your Apple TV a name so you can easily identify it when you use AirPlay. Just go to Settings > General > About > and select Name to change it.
To change the name of an Apple TV (2nd or 3rd generation), go to Settings > General > Name.