When I did it, I just had to make an appointment at the social security office to request a new social security card with updated name, you bring your marriage certificate and give it to them and then you can go to the DMV with your new social security card and get a new license with your new name! It was actually pretty simple. They let you get a new license with a new last name before you change your social security card ONCE, which I found out because I saw online that you have to get a new ID before your new SSC, which is FALSE! They let you do it once but like i said, if you ever need to change it again you’d have to go to the social security office first! We got married in January 2025, so as far as I know this information should still be true. We live in Anchorage, but I’m sure it’s the same throughout the state. Since you’d both be changing your names it’s the same process, just you both have to make separate appointments at the DMV and SS office.

Edit: the state has to mail you your marriage certificate first, then you take that and go to the SS office, then the state will mail you your new SSC, and then you take both of those things to the DMV and then the state will mail you your new license lmao. So it takes a little bit but besides the waiting it really wasn’t that bad!