No need to have a great brain in order to figure out the significance behind The Great Brain as our book's title. It's Tom's nickname, and though J.D. narrates, the book is Tom's story. So the title is a shout-out to Tom and his great brain.
There's another little detail to this, though. See, Tom pretty much invented his nickname himself—he refers constantly to his "great brain." While J.D. thinks he's pretty much the smartest guy on earth and earnestly calls Tom the Great Brain, Sweyn—who's older—uses the nickname with a bit more irony. Sure, Tom's smart, but Sweyn knows his limits, too.