@Noktor Not sure how you listed your fiancee's name on the DS-160 and K1 application, but if you did it as I had described above, her name should be listed in that order. Regardless, when she receives her Green Card, you could update her SS, but if she decides to change her name when she applies for naturalization, she/you will have tons of paperwork to fill out/mail to get her name changed to reflect her new name.
There are so many Vietnamese living in Fort Bend, Harris and surrouding areas, I am surprised they are giving you a hard time on the marriage license application.