Ladies who’ve gotten married and changed their last name..

So I went to the Social Security Admin office and changed my name to my husbands last name... I’m waiting for my card- but I want to know if I have to wait for my SS card or can I just go into the DMV and fill out the app for my new ID with new name? I read online that you don’t need to because the DMV can verify electronically through the SSA. I just want to make sure before I go stand in the long ass line for no reason!!