Please make the change before the 72 hour time line when the cruise line turns over the passenger manifest to Homeland Security for clearance.

The manifest is run through a computer program, which flags all "inconsistencies". You may get hung up trying to get on the ship explaining the disparity.

If I am not mistaken, you are from a country other than the USA, which will already put you under extra scrutiny. Call the cruise line, your TA, whoever booked the cruise, to make the changes so your name is consistent with your passport.