Since you are not a citizen, your identity will be based on your foreign passport and that is the name that will appear on your social security card. When you apply for your green card your original name will also be based on the name in your foreign passport. The best solution would be to see a lawyer in your country of origin and have your name changed so you can apply for a passport with your new name. If your name is changing because of marriage then you could apply for a new passport at your consulate or embassy here in the US with your new name by showing your marriage license. You could then apply for your social security card with your new name.
Answered on Mar 08th, 2011 at 10:03 AM