Q: Can't find my Apple TV underthe Airplay icon

Try the following steps, check whether things are working after each step where appropriate, before trying the next.

    1.    Check AirPlay is turned on on the Apple TV (turn it off and on if it already is)

    2.    Check that both devices are on the same network (Settings > Wifi, on the mobile device and Settings > General > Network, on the Apple TV).

    3.    Restart the Apple TV (Settings > General > Restart).

    4.    Restart the Apple TV by removing ALL the cables for 30 seconds.

    5.    Restart your router. (Also try removing it’s power cord for at least 30 seconds)

    6.    Restart your mobile device.

The following article(s) may help you.

Troubleshooting AirPlay

Troubleshooting Wi-Fi networks and connections

Recommended Wi-Fi settings

Wifi Diagnostic Software (for Mac users)

You may also find some help on this page, where I’ve collected some of the more unusual solutions to network issues.

I Had same issue.  The solution was the scroll down in the AirPlay device list and there was my Apple TV!  it's easy to not realise the list continues below because there is no scroll bar and full list is not shown , only the first two devices. 

That just sorted it for me....the simple things lol