How can I change my display name?

Hi, I have been on the phone with an apple rep and been to appleid.apple.com to try and change my display name on the support site. I see a myriad of user names of all variations and I really just want to change my actual full name (username) to just something generic. I am not sure this is possible or not and the apple rep did not have any solutions. Anyone have any suggestions? Thanks...John