You could add your wife as dependent in the Form DS160 and take a single slot for interview.
More information: [http://www.ustraveldocs.com/](http://www.ustraveldocs.com/)
I am not so sure about the impact or requirement of one's name on their spouse's Passport, related to VISA processing. In any case, you have more than 6 weeks to schedule the appointment (earliest is July 1st) and thus will get enough time to have your name added to your wife's Passport or the other way around. If you can do a urgent processing (called Tatkal or something), you could get the new Passport back in a week's time.new Passport in a week's tim