With your gift. Say Ssanders79 is in charge of it since he has the FE info. He would randomly assign a SM to everyone -- PM you with who you get to deliver to. You get the gift, deliver it, and it says who it's from on the gift tag. I have heard that some people have the stateroom attendant put their SM gifts in the room (especially if it's something that can't go into an FE). I have heard that a lot of people even wrap them like a gift, with wrapping paper and everything. I read a trip report that one family received a Lenox ornament for each member in their family! (I saw the orrnaments for $3.99 at Marshalls, so albeit a nice gift, they didn't spend a fortune).
That sounds like a great idea. We'll have to keep that in mind as the dates get closer and people decide on how many gifts they want to bring.