Get the SSN in maiden name, do not even say you're married. Do not bring the marriage certificate either. She can still get her social now but only in maiden name. Some SS personnel do not understand the K1. They think the K1 is voided if they get married. Rather than argue with them apply in madden name and when she gets her EAD she can do a name change then.
THis is why we say do it before getting married. They are clueless.