I have an international flight booked in my maiden name. Can I start my name change now?
Yes, you can start the name change process now. However, you'll need to wait until you return home from your international trip before updating your passport.
You won't run into any travel issues as long as the name on your passport matches the name on your travel reservations/boarding pass.
Your current passport in your maiden name will remain valid until its expiration date even if you update your name with the Social Security Administration or your DMV.