oh testo po . .. .   but u still look for a job and tilll the time u find a job, may be with next couple of weeks, you probably should get ur EAD card as if the name had only misspelled, which must not take long process from USCIS. But, when you recieve your EAD card, didn't you got a receipt also within that card. Check the name on that receipt also. If the name on the receipt is right then they should probably misspelled or misstyped while printing your card.

Isn't to apply for SSN, you need a job offer letter????? once you get a job offer letter then you can apply for SSN. I am not sure, but isn't that is the process.
I got my SSN way back where those days the UNIversity used to apply for our SSN on the first day we joined the school. My two roomates who have been going to school doesn't have SSN so far.