We got Jaycel's SSN about a week after she arrived (In her maiden name). This allowed us to add her as a joint account holder on my bank account and credit cards. Then when we filed the I-485 and I-765, we filled in her SSN where it asks on the forms, checked all the yes boxes (i.e.: "Do you want the SSA to send a new cad?) and used the forms to do her name change by putting her new, married name in the "Legal Name" section of each form. When her I-765 got approved, 7 days later she received her new SSN in the mail with her married name on it. (It still has the disclaimer, "Not Valid for Employment Without DHS Authorization", which is fine because she now has her EAD Card. We also did the SSN part on the I-485 so that, when approved, the SSA will send her a new card with that disclaimer removed.