However, because of the twist, I'm not sure how to narrate it. There are twins, and one dies. The reader, and everyone else, apparently, thinks it's one twin. The reader finds out part of the way through the story that it's actually the other twin, but only one other character in the story knows (and has known all along). Everyone else thinks it's still the first twin.
So, the question. Can a third-person narrator refer to the living twin as one name for part of the story and then switch names once the true identity is revealed to the reader? Does this then make the narrator untrustworthy? I can't imagine doing this as a first-person narrator, since it would either have to be the living twin or the person who's known all along, and I don't want the reader to find out until later.