Kaplan's (1989a) solution to the indexical version of Frege's Puzzle in terms of the character of linguistic expressions has been greatly influential and much discussed. Many philosophers regard it as being correct, or at least as being on the right track. However, little has been said about how character is supposed to apply to proper names, and how it could account for the name version of the Puzzle. In this paper I want to fill this gap. I sketch some solutions to the name version of Frege's Puzzle in terms of character, and argue that all of them are flawed in some way: they are either semantically implausible or fail to account for all relevant phenomena.1717580