I thought this problem was fixed when Apple fixed the network daemon problem last year. But my new Apple TV suffers. It's now up to 257 naming increments.
I can try that. I figured since it's a different name, I wouldn't have name collisions. But it's curious that the first AppleTV is no longer incrementing. It did prior to adding the new one.
This was a problem with OS X Yosemite, fixed when they dropped the new "discoveryd" for the old daemon. I thought this fixed the issue conclusively. But I now recall some internet discussion about AppleTV still running old networking software and continuing to have this problem. Another possible fix is to give them fixed IP addresses at my router. But I'm using an Airport Extreme, so I don't know if I can do that.