Symbolism, Imagery, Allegory
In Egyptian magic, names grant power. Here's how Thoth explains it: "Everything in Creation has a secret name… Even gods. To know a being's secret name is to have power over that creature" (23.148). So names are a big deal.
When the kids are on their way to the Land of the Dead, Sadie faces Shezmu (the demon with perfume samples) and has to figure out his secret name in order to pass without becoming a snack. Sadie's quick-thinking skills help her trick Shezmu into revealing his secret name, which means they get to… pass into the Land of the Dead without actually dying. Yay?
Maybe Sadie's good at figuring out secret names for a reason, though. According to Thoth, Isis tricked Ra into revealing his secret name, and thus forced him to pass the throne to Osiris. This made Set jealous and kicked off the whole Set-became-a-bad-guy thing. Not so good.
However, when Sadie rises from the red pyramid to change the course of the battle with Set, she realizes that she's come into her own as the blood of the pharaohs, and also as "Isis, goddess of magic, holder of the secret names" (40.4). Maybe Sadie's talent for secret names has something to do with the fact that she's hosting Isis, who's already a whiz at them. As much as Sadie hates the thought that Isis might be controlling her—well, there's something to it.
And, of course, the quest to find Set's secret name in order to defeat him is one of the major plot points of the book. So to recap: names are important, secret names triply so. Better be careful to whom you reveal your name if you're going to be hanging out with Egyptian magicians and gods.