What’s equally important is this: “NOTE: In some cases an individual’s sex may impact eligibility for benefits dependent upon spousal relationships. To make title II entitlement or title XVI eligibility determinations dependent upon marriage, follow the instructions in GN 00305.005B. Do not use sex field data on SSA records to make marital status determinations.” This means that if you change your SS record, it will NOT change your benefits eligibility, only the actual legal status of your marriage changes it.

via SSA – POMS: RM 10212.200 – Changing Numident Data for Reasons other than Name Change – 06/13/2013.