Definitive description associated with the name. Necessary and sufficient condition. It is true in general if we think of those descriptions as fixing the reference of the term, but not giving the meaning . But we are not referring to Schmidt, but to Goedel. What is relevant is the actual chain of communication.
Proper names are rigid designators.
A possible world isn't a distant country that we are coming across, or viewing through a telescope. A possible world is given by the descriptive conditions we associate with it. Possible worlds are stipulated, not discovered.