Low

I been a US LPR since July of 2011 ... I recently started a new job and I was filling up my W2 form with Human Resources. After filling the form HR calls me back and tells me to fill the form with the name as shown in my SS card .After all this time i had never checked my SS card name just the number. My Green Card and Passport have the correct name but my SS card does not . What are the steps to take to correct the spelling ? also is this going to be a nightmare to do ?

Thankyou for giving me peace of mind !!...

Hello

So heres a brief look at my history,My Grandmother is a USC and petitioned for my farther in 1994,I was 11 years old.My father petitioned for my mother and me and my other brothers. Honestly i had forgotten all about it until last year when my Mom calls me , am 27 now, and said that we all got our interviews and medical appointments and what not ,long story short we all got our GC now except my older brother cause he got married,so changed status(saddest and happiest day of my life),I just got back from Miami ,currently in Dominican Republic.In miami I went and got my Social,GC and a spanking new Driver license.So am moving for good next moth on the 15th .My question is i have a long time Girlfriend ,we have been living together for a longtime I never got married because i always hoped of getting my LPR ...Heres my question, My GC is a F33 category ,can i petition for my soon to be new wife and son to be born daughter,due on the 23rd of this month, as soon as I get back to the States ?