If the music on your artist page is correct on Amazon Music, then it is possible that your artist name was delivered incorrectly. To update your artist name you'll need to work with your label or distributor to make the requested changes and re-deliver to Amazon Music.
If you are having issues updating your name have your distributor reach out to their Digital Operations Manager.
If your artist profile has other artists music....
If you are seeing music on your artist profile that does not belong to you or your music is on another artist's profile, then it is possible that the name displayed belongs to another artist. If this is the case, let us know that your profile requires attention using the Report Issue tool in Amazon Music for Artists, under User Settings.
You can use this tool even if you have not been able to successfully claim your artist profile in Amazon Music for Artists.