Well, if the passport isn't expired yet, you could fill out the form for the lost passport.

A name change is handled by submitting a notarized copy of your marriage certificate. At least it was back in the dark ages when I got married... but then, times have changed since then.

If you choose to apply for a new one, same thing - submit both your birth certificate and your marriage certificate. The first time I had mine changed, they simply added a page at the back that said something like "Passport amended to" and listed my married name. But that was keeping my original one. When that expired and a new one was issued, it was simply in my married name.

I'm sure someone will chime in with more details.