How do I merge my library with my new apple music "This Computer" library?

I have two libraries on my iTunes on my Mac. The old "My Computer Name Library" and now the new "This Computer" library. The new library is linked to my Apple Music account, and as such crosses all my devices via iCloud. But I am unable to access the new library on my Apple TV as it won't recognize it as a computer, just the old account. Any suggestions? I've rebooted all systems and it still seems to be the same.