 A rigid designator designates by picking out its designatum not just with respect to the actual world—as things are—but with respect to all other possible worlds in which it is present, as well. That a proper name like your name is rigid by way of picking out its same designatum (you) with respect to possible worlds or situations different than those actually obtaining, though that claim is not without detractors, is a claim that enjoys great appeal. Call the relevant claim “transworld identity.” The claim is associated with a host of others that might enjoy much less appeal. Many such claims turn out to be separable from rigidity. Nevertheless, transworld identity remains a substantive commitment of rigidity, at least as classically understood.