Yes, you'll get a luggage tag as a part of your documentation from the cruise line. You can print these out and attach them to your luggage - suggest using some clear tape to make them a little less fragile.
Or you can wait till you get to the pier and the luggage handlers will have a supply of better luggage tags and all you really need to put on them is your cabin number. This is what we prefer to do instead of using the paper ones.
As for your passports, you don't have to have them for a closed-loop cruise - meaning a cruise then starts and ends in the same U.S. port and goes to Canada, Mexico, the Caribbean, Bermuda, or the Bahamas. All you need is an original birth certificate and a photo ID, such as a driver's license. That way you can wait until after you're married to get your passports with her married name.
However, I always suggest getting a passport just on the off-chance you have any problems in a foreign port and have to fly home. But in this case, it's not needed and the overwhelming people cruising don't have passports, so don't feel like you have to rush out and get one, especially if your budget is tight.