If you legally change your name because of marriage, divorce, court order or any other reason, you must tell Social Security so you can get a corrected card. You cannot apply for a card online. There is no charge for a Social Security card. This service is free. The same applies once you receive the I-766 card, Employment Authorization Document (EAD), from the U.S. Citizenship and Immigration Services (USCIS) and bring required evidence. See Defining the legal Name for an SSN .
To get a corrected Social Security card, you will need to: