In order to change your last name after marriage, you have to first obtain a copy of your marriage license or certificate. Make sure to get a new social security card. This is crucial. The new card will show your new name, even though your SS number will not change. Take your proof of marriage and SSC and submit it by mail, or by hand to your local office. Make sure to show these things to your workplace, or any other place that will need your new last name. Then, your set!