Yeah, I have a similar situation... but mine is 'in house'. I have 3 Apple TV's.... if I'm watching TV in my bedroom my grandkids, AND daughter, will try to 'airplay' something from their phones, usually a game, and instead of choosing the living room Apple TV they choose mine.... shutting me off.

I tried to fix it by renaming the bedroom Apple TV "NOT THIS ONE"... it didn't work.

So I tried renaming again to "NO NO NO DAMN IT".... partial success with that one but no guarantee. - JamesJM