apple tv

If you mean the devices list for your account, separate from any functionality,

Check your Apple ID device list to see where you're signed in - Apple Support

then devices with Apple TV system software 7.x or later should show up [1], if signed in to the iTunes Store on that device (Settings﹥iTunes Store﹥) [2].

If you mean the Find My devices list, then no Apple TV boxes are included there, as their location isn’t tracked.

See: If screen mirroring or streaming isn't working on your AirPlay-compatible device - Apple Support

Verify that AirPlay is turned on in Settings﹥AirPlay of the Apple TV box.

Recommended settings for Wi-Fi routers and access points - Apple Support. Verify that both devices are on the same home network. If your router uses different SSID network names for the 2.4 GHz and 5 GHz band, then those parts may be seen as two different networks that do not communicate with each other. If, so, then it is best to bridge all home network parts as one logical network, and not use different names for the bands.

Else contact the support staff.

What is your model Apple TV? Identify your Apple TV model - Apple Support

Verify Settings﹥General﹥About﹥.

If it says ‘Activation: Failed’, then see: discussions.apple.com/thread/253315520 for a remedy.