I have read/tried all below and cannot display Mac El Capitan screen on Apple TV 4 - the Airplay icon is never visible. All apps/OS are latest. Apple TV returns (on TV Screen) select 'Living Room", which in name I assigned to Apple TV
Use AirPlay to display video from your Mac on an HDTV
Stream video from QuickTime Player or Safari
In OS X El Capitan, you can stream certain videos to your Apple TV from Safari or QuickTime Player (version 10). Just click the AirPlay icon —if available—in the playback controls, then choose your Apple TV.
OS X El Capitan: Use AirPlay to see your desktop on an HDTV
Before you begin, see the Apple Support article Use AirPlay to display video from your Mac on an HDTV to find out if you can use AirPlay Mirroring with your Apple TV and Mac.