Are you using an @iCloud address that is already associated with your Apple ID?
you can enter an @icloud.com, @me.com, or @mac.com email address that's already a login alias or alternate Apple ID for your account. To see these addresses, sign into your Apple ID account page. Click Edit under the Account section to reveal Reachable At. In this list, a login alias will have a next to it which, when hovered over with a mouse pointer, shows this message: “This is an alias of your Apple ID email address.”
Apple ID Name Change
What to do after you change your Apple ID or password - Apple Support I suggest doing this before you change your Apple ID or password.