As Sandy stated, I don't think you'll need the reservation number. I can give you an example of what happened to me. I was sailing on the Freedom of the Seas last year. My sister sends me a text message, asking what the name of the ship was, and the sail date. I give her that information.
On embarkation day, after I get checked in, and go to my room, I see on the desk a "Happy Birthday" note from her, along with an onboard credit from her, which was her birthday gift to me. It can't hurt to have the reservation number, but what I assume happened, was my sister called Royal Caribbean, gave them the passenger information, ship name, and sailing date of the cruise to have that gift delivered. I booked directly through Royal Caribbean at the time, and not through a travel agent. I don't recall giving my sister my cabin number.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)