Airplay: Devices "bedroom" and "main Bedroom" Showing up

I don't think that you have done anything wrong.

As far as I can tell, the devices "announce themselves" using Wifi and Bluetooth - but in order to actually use them, you need to be in the same Wifi and, depending on the configuration, also enter a code, or be connected to the same Apple id, for example. The point is that by merely seeing that there is an Apple TV nearby it does not mean that you can actually use it.

I have an Apple TV and I can see it in my iPhone when I am close, even when the iPhone and the Apple TV are connected to different Wifi networks. However, in that particular circumstance, I can't do Airplay to it - and you probably also can't Airplay to your neighbor's Apple TVs.

I see all my neighbor's wifi networks but I can't log into them unless I know the password. If a network or device is broadcasting its presence then you will see it just as others will see your network if it is broadcasting its SSID.

Most likely they are from a neighbor.