I am having the same issue and I am beyond frustrated. I have a MBP running iTunes 12.4.3.1 and an AppleTV4. I have rebooted everything (ATV, MBP, AirPort Extreme), set the ATV to DHCP, reset the home sharing on iTunes and the AppleTV. No joy when I try to connect to the "Computer" icon on the ATV.
When I go to the Music icon, I see about a third of my music that is in my library - 3300 songs versus the 9800 songs. If I can not see my computer in home sharing, where is the music coming from? Can't be from the iPhone - I only have 2800 songs on that.
I am at a complete loss to why I can not see my computer. Now, not sure if this has anything to do with it, but when I first turned the ATV on it wanted my password. Using the remote - and the correct password - it kept faulting back for me to enter my password. It wasn't until I got so fed up (more than 5 times) that I went to the remote app on the phone and entered it that way - and it took.
Any help would be greatly appreciated.
Thanks