Have you visited our lovely "Symbols" section yet? We have quite a nice write-up about Surrender the dog over there, and we highly recommend that you check it out. It definitely cracks Surrender as the book's title, open—you know, if we do say so ourselves.
Here we just want to add one small point: The book is, well, bookended by dying. And in this way, though it takes us pretty much the whole stinking thing to realize, the story is about Gabriel accepting that Finnigan is a part of him—surrendering to this terrible truth—and then surrendering to the only viable solution for ridding the world of this evil: death.
But really, check out the "Symbols" section for more. The title might only be one word, but it packs a punch.