Salutations alexandru-florin,
It would be helpful to know what’s happening on your device when this prompt appears. For example, are you attempting to download apps, update apps or something else?
If you haven’t already, try entering in your Apple ID password. Should you receive an error message, let us know what it says. Since you mentioned changing only the Apple ID and not the password, it may recognize the current password.
You can also check in Settings > your name and Settings > your name > Media & Purchases to be the correct Apple ID shows there.
The following article also has steps to take after changing your Apple ID - What to do after you change your Apple ID or password
Thanks.