There is no fee required to receive a social security card with your new married name. You will, however, need to visit a local Social Security office and apply for your new card in person. You will need to bring your marraige certificate with you as well as an identifyng document with your picture on it such as a driver's license, state issued I.D. card, or an U.S. passport. You must also show proof of U.S. citizenship in the form of a U.S. birth certificate, U.S. passport, certificate of naturalization, or a certificate of citzenship. All of these documents must be originals or certified copies in order to be accepted. Form SS-5 can then be obained and completed at the office and you will receive your new social security card in the mail within ten business days.