Apple ID

You can delete your Apple ID by following the link below. Make sure you read the support article thoroughly as this is permanent and you could experience data loss. I don't know if deleting the old Apple ID will remove the message you are seeing.

How to delete your Apple ID account - Apple Support

With the "Update Apple ID" message in settings, it would appear you have that ID on your device somewhere. Is it possible that you have an App that was downloaded with that Apple ID at one time. There is no easy way to determine if an App was downloaded with a different Apple ID, but a message will come saying it was purchased with a different ID when it is updated. You could try guessing if an app may have been downloaded with that ID and delete it. They can always be downloaded again if they were using the correct ID.

Here are some other locations to look:

• Go to Settings > [name on top]. Is that Apple ID listed under "Media & Purchases"?
• Is the old Apple ID listed at Settings > FaceTime. Under the Caller ID section, it will show an Apple ID.
• Under Settings > Music, do you have a "Home Sharing" section on the bottom with the old Apple ID?
• Go to Settings > Messages > Send & Receive. Verify the Apple ID on bottom as well and the send & receive addressees.
• Go to Settings > Game Center. Review the address used for Game Center on the top of that page.

Some users have reported they they were able to solve the problem by signing out of your Apple ID on all devices that you may have, then signing back in after a Force Restart of the device. Force restart iPhone - Apple Support

I do understand you are using your correct Apple ID at Settings > [name on top]. My point was that there are at least 5 locations as provided in my previous post where your old Apple ID could still be used, which is the reason for the prompt you are seeing in Settings. I'm not sure if you have reviewed those locations. The much forgotten about one is Game Center where it is very possible you could be signed into your old Apple ID there, while still using your current Apple ID that shows in the Settings page. At the bottom of the Game Center page, it gives you the option to Sign Out, if it is showing your old Apple ID.

The other instance of having an app on your phone from when you had your old Apple ID is possible. When you sign out of your Apple ID, it does not delete the apps that you had downloaded. They will stay there even if you sign back in using another Apple ID. If you were to try and update the old App it will ask for the old Apple ID password to continue. This is why your old Apple ID would still be attached to your device prompting the Update Apple ID in settings. In this case, removing the app would remove the need for the prompt to update your Apple ID in settings for your old Apple ID.

It is also not unusual to be using your main Apple ID and use a different one in the Media & Purchases section. Apple deleting your old Apple ID will not remove it from your device if it is in one of those locations. This would have to be done by you.