I provide a novel semantic analysis of proper names and indexicals, combining insights from the competing traditions of referentialism, championed by Kripke and Kaplan, and descriptivism, introduced by Frege and Russell, and more recently resurrected by Geurts and Elbourne, among others. From the referentialist tradition, I borrow the proof that names and indexicals are not synonymous to any definite description but pick their referent from the context directly. From the descriptivist tradition, I take the observation that names, and to some extent indexicals, have uses that are best understood by analogy with anaphora and definite descriptions, that is, following Geurts, in terms of presupposition projection. The hybrid analysis that I propose is couched in Layered Discourse Representation Theory. Proper names and indexicals trigger presuppositions in a dedicated layer, which is semantically interpreted as providing a contextual anchor for the interpretation of the other layers. For the proper resolution of DRSs with layered presuppositions, I add two constraints to van der Sandt's algorithm. The resulting proposal accounts for both the classic philosophical examples and the new linguistic data, preserving a unified account of the preferred rigid interpretation of both names and indexicals, while leaving room for non-referential readings under contextual pressure.