klam133

I believe you apply for the SSN as soon as she arrives in the US. Look at the guide here on VJ, it tells you all the documents you'll need

I think most will say that legal name changes should wait until the entire immigration process is finished . . . through citizenship.  Otherwise, you are producing another set of documents that will require additional proof that" document A" is the same person on "document B."  Furthermore, the Vietnamese consulate/embassy may not accept the name change when it is time to request a new passport.
 
Jason

You need to contact the embassy first as it's the embassy that has halted the process. Once (and IF) the embassy gives you the green light they will let NVC know so NVC kan send your case to the embassy.