If there are several devices connected to the network, you can get confused between them. To avoid confusion, simply rename the devices. You can easily rename the Apple TV and add customized name the way you want to. The new name will be displayed on the network afterwards.
For this purpose, follow the steps below:
- Open Settings -> AirPlay -> Apple TV Name
- Enter a new customized network name for your Apple TV
Now, whenever you will connect the Apple TV, you will be notified on local network by its name and there will be no issue at all.