If you legally change your name because of marriage, divorce, court order or any other reason, you need to tell Social Security so that you can get a corrected card. If you are working, also tell your employer. If you do not tell us when your name changes, it may:

Delay your tax refund; and
Prevent your wages from being posted correctly to your Social Security record, which may lower the amount of your future Social Security benefits.
If you need to change your name on your Social Security card, you must show us a recently issued document as proof of your legal name change. Documents Social Security may accept to prove a legal name change include:

Marriage document;
Divorce decree;
Certificate of Naturalization showing a new name; or
Court order for a name change.
If the document you provide as evidence of a legal name change does not give us enough information to identify you in our records or if you legally changed your name more than two years ago, you must provide Social Security with additional documentation.

Marriage, divorce or annulment: In addition to showing us a legal document proving your marriage, divorce or annulment, you must provide an identity document. That document must show your old name, as well as other identifying information or a recent photograph. (We can accept an expired document as evidence of your old name.)

Adoption, naturalization or other name change: In addition to showing us a legal document citing your new name, such as a court order, adoption decree or Certificate of Naturalization, you must provide us with two identity documents, including:

One identity document in your old name (which can be expired); and
One identity document in your new legal name, which must be current (unexpired).
Both of these documents must show identifying information or a recent photograph.

Citizenship: Also, if you are a U.S. citizen born outside the United States and our records do not show you are a citizen, you will need to provide proof of your U.S. citizenship. If you are not a U.S. citizen, Social Security will ask to see your current immigration documents.

Your new card will have the same number as your previous card, but will show your new name.

The information provided on this page was obtained from Federal Citizen Information Center: http://www.pueblo.gsa.gov/