The very end of the book, from the final paragraph (Epilogue.44), is a neat bookend to the very beginning of the book. As you remember (because you're not Jason Bourne), The Bourne Identity starts with some anonymous dude getting shot at sea and falling into "the madness of the darkness below" (1.4), where he loses his senses and his self. It's all about water, violence, water, wounds, water, dark, water, loss, and water. So yeah, there's some water symbolism: you go under and you float away.
The end of the book also has the water symbolism. Bourne's out on the beach with Marie watching him. Lots of guys with guns are standing guard. He's healing from his injuries nicely and idly skipping seashells…and then he runs into the waves, shouting.
Marie, having lived through the rest of the book, is aware that sudden movements and shouting are bad, bad things, and she naturally assumes there's an attack of some sort, or at the least an errant angry banker flopping about like a beached walrus in the shallows.
But, in fact, there are no bad guys and no errant bankers. There's just Bourne, happily running up the beach towards her, to tell her that he's remembered his name—which is (as we already know, but he does not) David. Going into the water in the beginning was a birth into nothingness; coming out of the water here is a rebirth into something possibly real.
"Hello, David," Marie says, as if she's meeting him for the first time. Hey, actually, she is meeting him for the first time, and we are too. It's taken the book and a lot of time and whole lot of dead bodies, but at the end, we finally, finally get to greet our protagonist.
He's damp but cheerful.