Did you receive your employment authorization card? If you want to change the name on that card, you would need to file a request with USCIS. To change your name on your Social Security Card, go to a Social Security office with your marriage certificate and ask for a name change. Social Security might tell you that you need to change your name on your employment authorization card.
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You may have to request USCIS to change your name on your EAD as theis often requested by SS offices. Although you should really be allowed to change your name with your marriage certificate, I'd and EAD card.http://ssa-custhelp.ssa.gov/app/answers/detail/a_id/315/~/change-a-name-on-a-social-security-card