Hello djpozzi,
Okay, so it's just when you go into the Music application that you see this other Apple ID. It sounds like you may be signed into the Media & Purchases option with this different Apple ID then.
Go to Settings > name at the top > Media & Purchases, in the options that come up select View Account. Then at the top of that page check to see if it's showing the same Apple ID that you've been seeing in the Music app. If it is, select Done to close the window then select Media & Purchases again and this time select Sign Out. Once you're signed out, sign in to the Apple ID you want to use for Music.
In a Family Sharing group, you can also check to see if the purchase sharing Apple ID was possibly changed there which would cause a different Apple ID to show up under Music.
Use a different Apple ID to share purchases with Family Sharing
Cheers!