Appellation is a supposition restricted to presently existing things: appellatio est acceptio termini pro supposito vel pro suppositis actu existentibus (de Libera 1982:252). It corresponds to what we could call actual denotation. It is not an intrinsic property of a term, but a syntactical limitation of a certain type of accidental supposition, namely, of personal supposition: contrary to Peter of Spain, Lambert does allow appellation only for common (and not for discrete) terms. Appellation is itself divided according to the divisions of personal supposition: we have determinate appellation when a common term stands only for one among its presently existing supposita (as in homo currit), and distributive appellation when it stands for all of them (as in omnis homo currit - de Libera 1982:255256). Furthermore, Lambert does not accept the rule of the sufficientia appellatorum stipulating that at least three appellata are always required: according to him, a single appellatum is sufficient. And in case there are no appellatum at all, Lambert allows for a term to stand actually for a non existent entity (de Libera 1982:257, as well as Goubier 2000:50 and 57).
See also: > Logic > Peter of Spain > Roger Bacon > Supposition Theory > Universals > William of Sherwood