The "real" answer may not be the one you want to hear. Yes, you do need to have your birth certificate and a copy of your marriage certificate to show the name change.
The sad part is that you may not have to show your marriage certificate but if you are asked for it and can't produce it YOU WILL NOT board the ship.
You should contact the county courthouse or hall of records of the county you were married in and get a copy of your marriage license. Do it as soon as you can.
Also if you are going to cruise the Caribbean next year, or Canada in 2007 you will be required to have a passport.