Newly married. Last year we filed separate. This year we filed together. They rejected ours because they said her last is not correct. Does she file with my last name?

She needs to use whichever name she currently has listed with the Social Security Administration. If when you got married she changed her name, she needs to file with that name.  If her name was not changed and she is using the same last name as she had prior to getting married then she will need to contact Social Security Administration at 800-772-1213.