Water in The Bourne Identity is generally associated with rebirth, when Bourne gets reborn and so on.
Yeah, we went there. But so did Ludlum, so we're just going to own it.
At the beginning of the book, Bourne gets dumped in the ocean and comes out innocent as a baby, memory-less and pure. Well, as pure as you can get with a history like that, anyway. At the end of the novel, Bourne goes running into the sea at the moment he remembers his name. And do you remember what he does when he leaves the Doctor Washburn and finally ventures out on his own? That's right: he swims naked in the water to the shore of France and lies down in the sand, at which point the text helpfully tells us: "The day was being born, and so was he" (3.41).