How did you book your trip? Was it under your married name or maiden?
If you have time before your trip, get a passport. I think the current travel restrictions are requesting one. I would call the cruise lines or any travel agent like right now & find out what you need. Gone are the days when a birth certificate was valid.
Also, there's been a few reports of people being denied boarding on a few cruise lines because they never changed their information over to their married names (passports & such).
I really, really, really suggest you get a passport. It'll save you a ton of headaches & if you plan on any future travels outside the U.S., you are going to need one anyway.