A device works with one person's Apple ID. I want to change the Apple ID of that device to mine. We have signed into that device with its existing Apple ID. How can I change both user name and password of that Apple ID to mine?
Start here.
What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support
Then, assuming both you and your wife already have your own, independent Apple IDs, “move in” using the new ID.
Perhaps you’ll choose to implement Family Sharing.
What is Family Sharing? - Apple Support
How to change iPad Apple ID from my wife to mine
