LOST thought.
Maybe our heroes' hatch is called the Swan because of the way they have grown by being there.
Ugly Duckling --> Swan.
These are characters who are all very much flawed. The Others have identified themselves as "good people" -- maybe in order for our Lostaways to be good, they needed to have that experience in the hatch. I mean, Locke went from believing in it (blind faith), to not believing in it ("scientific proof" of the Pearl)...
but wait.
Pearl's go through dramatic changes as well. Don't they start out as sand and then over time, they are formed into pearls? Again, the process of change and growth. It's a possibility, I guess?