Thanks for the answers. For the ssn:
Yesterday, I went but wrote down my new last name. As soon as the lady looked at the application and my I-94, she said she needs the 'name to be on card' to match my I-94. She tolde to go to immigration and change name on I-94 to new last name. Confused, I went home, called immigration, asked if its possible to change name on I-94, got told its not possible.
SO.....
Today went back to ssn, used maiden name, and TAA DAA! Got letter saying I'll have it in 2 weeks:)
From my research, found out tht when u change ur name when getting marriage license, it doesn't automatically change ur last name just like that. You have to go through a different process to do so.
SO... When I receive my ssn, I'll wait for my green card, then get name on ssn changed.
Just for those who r planning on getting ssn after marriage.