Unknown Applie ID

Check the App Store and iTunes Store to see if there are any updates for apps/purchases. A request for an old Apple ID password is often caused by updates to apps/purchases that were made when using the old ID. Those purchases are tied to the old ID and can't be transferred. One option is to delete the apps/purchases made by the old ID and download them using the new ID if desired.

You can't delete an account, and I'm not aware of any easy way to find what item you have from that account is causing the popup to show. You could go through your account's purchase history and see if there is anything on the phone not on it : See your purchase history in the iTunes Store - Apple Support