When we went on our cruise in December, we brought along our adopted son. We adopted him in September, but had not yet received any paperwork from the court. We had nothing stating he was ours. The only thing we had was his original birth certificate listing his bio parents information. We purchased the tickets in his bio name and did not change it to his adopted name because we didn't have any new paperwork. No one batted an eye either at the airport or Carnival about his name being different, etc.
My bio daughter's father left when she was 2 and we haven't heard from him since. My husband adopted her. We have always traveled and never had anyone ask for consent from her absent father. We have also taken other people's children on vacation with us, and the only thing I usually bring along is a consent from the parent's for medical care. I also send the same along when my children vacation without us.
That being said, I do agree with the other poster's about checking with Carnival directly and getting it in writing. What one person tells you at Carnival may be completely different with another person from Carnival.
02/13/05 Carnival Miracle
12/27/03 Carnival Triumph
02/15/03 Carnival Inspiration