My aim is to show that once we appreciate how Searle (1958) fills in the details of his account of proper names – which I will dub the presuppositional view – and how we might supplement it further, we are in for a twofold discovery. First, Searle’s account is crucially unlike the so-called cluster-of-descriptions view, which many philosophers take Searle to have held. Second, the presuppositional view he did hold is interesting, plausible, and worthy of serious reconsideration. The idea that Searle’s account is a largely Fregean interlude between the Fregean description theory of proper names and Kripke’s proposals presented in “Naming and necessity” is in major ways a myth, a mythical chapter in how the story of 20th-century philosophy of language is often told.