After changing your name through a court order and/or updating your birth certificate, you will also need to file for an amended Social Security Card with the Social Security Administration.
You will be required to provide evidence of your legal name change, your identity and your U.S. citizenship and complete an Application for a Social Security Card (Form SS-5). Evidence of legal name change includes a court order of name change. A document showing your name, identifying information and photograph, may be used to confirm your identity, and may include any of the following documents: driver’s license; state issued non-driver’s identification card; passport; employee or school identification card; health insurance card; or military ID. Your citizenship may be evidenced with any of the following: U.S. birth certificate; U.S. passport; Certificate of Naturalization; or Certificate of Citizenship.
Informational links on name changes with the Social Security Administration
Link for Application for Social Security Card