I don't think you can unless you get your name legally changed. It is the same as when someone gets married. Until the persons last name is legally changed with proof of documents then the system will keep what name you have on your legal state documents.
You will need to file a petition with the county clerk. Make sure you have it notarized. And the clerk will give you a court hearing for a judge to approve and sign. Then you can take this info after approval to the social security office and have your name changed for your SS# also and update any IDs you have with the new name. Look up more info for your state. Every state varies. I believe you can even get a new birth certificate with the name change also.
Hope this helps a little.