Try your iCloud email address.
Thats what i am using cause as i said i dont have a username on youtube... i login only with my icloud email. On apple tv it says put your username....
I meant just put your email address in the username field. It will work.
Just a friendly note, don't reveal your email addy on the internetYeap.... i put just the email and it is not working.
This is the way i am signed in youtube.
do you have 2 step authentication enabled on your google account?
if you do then you will need to create an application specific password for the appletv.
I dont trust google... i have also skipped the part in the registration where it aks to add our mobile phone number....i didn't create youtube channel cause it auto creates google+ profile.... so i ll have to live with that... no youtube profile for me on apple tv.
Honestly, if you have a device that can do it, it's best to to just AirPlay YouTube. The iOS app is much better than the one integrated into Apple TV. (you may also be able to find a plug-in for your browser that'll allow it to airplay YouTube videos)