How do I change my mail name?
Note the restrictions in the article.
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.
Thank you for posting in Apple Support Communities. From our understanding, you would like to change the name on your Apple ID, do we have that right? If so, check out the steps here: Change your Apple ID to edit your Apple ID information.
You can also check out this article on what to do after you make changes to your Apple ID: What to do after you change your Apple ID or password.
Hope that helps!