Name Change and AppleID

Why are you creating a new Apple ID? Why not just change the name on the old one? You want to avoid creating a new account if at all possible. Doing that means you will lose some content, and transferring the rest is a big nuisance. Simply update information on the old one.

To change your name associated with your Apple ID:

1. Go to https://appleid.apple.com/

2. Authenticate

3. Click Personal Information

4. Click Name

Or: Settings —> Apple ID —> Personal Information.

Read this article about managing the information you use with your account --> Manage and use your Apple ID - Apple Support

Again, there is no need to change to a different account. Simply change the information used with the current account. If your name is part of the email address you use as your account username then set up a different email address that isn't using your name. If this is an iCloud address, that's a bad idea using an iCloud address as your Apple ID address. Get one from somebody else. If your iCloud address has your old name in it then use an alias instead (you cannot change an iCloud address).

I provided links about this earlier. Here's another one:

Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support

Some countries let you use a telephone number as an Apple ID but in 20 years I have never seen anybody mention being able to change from using one to another kind.

If you feel you must, you can create a new account but then you will need to read several very long posts here about how to work with using two accounts (and I would have to spend 30 minutes replying to just your one question). It would be MUCH easier to just change the information used with the original account.