Yes I'm sure I can help you. Have you changed your name or recently become a U.S. citizen?
Neither of those things, no.
I am a foreign student F-1 and would like to work on campus. Do I need a Social Security Card?
Yes and you must provide a letter from your designated school official that confirms your identity and   your current school status.
When I am working how would I proceed if I need to change my name?
You must notify us as well as your employer.
Does the letter from my employer need to have my new name?
Yes the school official must use the correct name on your status letter.
Will I receive a new card with my new name?