In this paper, I will focus on the debate between descriptivism and antidescriptivism theory about proper names. In Section I, I will propose an historical reconstruction of the debate, and I will focus in particular on Russell and Kripke's treatments of proper names. Some criticisms will be advanced against Kripke's hypothesis of rigid-designator and, more clearly, against the consequent distinction between the epistemic and metaphysical level that Kripke proposes to explain identity assertions between proper names. Furthermore, I will argue, that, (...) pace Kripke, Russellian treatment of proper names allows to capture all our semantic intuitions, and also those semantic interpretations which concern context-belief sentences. I will close Section I by focusing on a criticism that Kripke rightly points out against an example that Russell proposes in his On Denoting. Section II will be devoted to Russellian solution: I will show that not only Russell's logical treatment of proper names allows to answer to Kripke's criticism to Russell's example, but also that such treatment can disambiguate and express all our semantic intuitions about Frege's puzzle sentence “Hesperus is Phosphorus”. I will then show that, contrarily, Quinian solution (discussed in Section III) and Kripkian one (see Section IV) are not satisfactory to capture our semantic knowledge about Frege's sentence. Furthermore, in Section IV I will focus on Kripke's distinction between epistemic and metaphysical level to deal with identity assertions between proper names, and I will logically show that such distinction is not plausible. In Section V, then, I will show that Russellian solution allows to explain context-belief sentences, contrarily to what Kripke thinks. In VI, I will summarize what I have argued in the text and I will draw some morals. (shrink)