Random Apple ID requested on new iPhone set-up

Your solution will work to a point. But every time one of those apps has an update available, you will still be required to enter the Apple ID Password for the previous Apple ID you once had in order to update them. When that happens, you should deleted the app you can't update and rebuy it under your new Apple ID. Remember that apps are forever tied to the Apple ID they were downloaded under.

It used to be possible to view the Apple ID associated with the App when plugged into your computer and using iTunes under the Files tab. You used to see a list of all the apps installed along with the Apple ID, but not sure if it is still possible. If there is one there that is not your Apple ID, then delete it to avoid any future problems.

CHCkiwi wrote:

Understand what you are saying however I have never acquired an app under another Apple ID. Also this requirement never appeared when installing iOS upgrades to my iPhone 11. Only appeared on transferring to iPhone 14.

Time will tell

You can count on the fact that when its time to update these apps, you will be asked to update them using the Apple ID they were downloaded under. It's not a maybe. Hence why two of us have now recommended you delete those apps and buy them under your new Apple ID. Changing one's Apple ID is always the wrong thing to do.