At least since Kripke (1980) it has been generally accepted that true identity statements involving proper names are necessarily true. This view is allegedly supported by our most ordinary, pretheoretic intuitions according to which ordinary proper names are rigid designators. This paper challenges the established status of this view. Section 1 develops the context of the debate by presenting the intuitions of rigidity and of contingency of identity found among competent speakers. Section 2 shows how the latter constitute a serious problem for the received view, one that cannot be easily ignored. Section 3 considers three available proposals intended to solve the problem and shows why they fail. Section 4 briefly describes a way to make com...