Does anyone know how to remove a phone number from my Apple ID and register a new one instead of it?

You need to change the number on your Apple ID. After the change, allow up to 24 hours for the change to sync. Before trying to make the change, sign out of Messages/FaceTime on all devices/computers.

Apple ID - Manage       

Lkrom Said:

“Does anyone know how to remove a phone number from my Apple ID and register a new one instead of it?”

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Reassigning eMails to your Apple ID:

To get this to go through, you would need to add the new address first, and then delete the current one.