Why does my new phone ask me to log in to apple ID that is not mine?

Is the other account totally unknown to you? If so you should report it to Apple's security team.

While I don't have a solution I have had the same issue for many many years when my girlfriend bought an album on Music Store using her account on my phone. I have tried to remove the album many times but it seems to be stuck somewhere.

Luckily we are still living together so I can ask her to login every time I restore to a new phone.

You'll need to figure out which apps on the old phone were purchased under a different Apple ID and delete them then back the phone up again. If you try to update apps on your old phone, you should be notified of ones that can't update without a different Apple ID than the one the phone is currently using.

Glad to hear!