Full Idea
I will call something a 'rigid designator' if in every possible world it designates the same object, ..and I will maintain the intuitive thesis that names are rigid designators.
Gist of Idea
Names are rigid designators, which designate the same object in all possible worlds
Source
Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 1)
Book Reference
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.48
A Reaction
The immediate problem seems to be objects that change across possible worlds. Did nature rigidly designate Aristotle (e.g. by his DNA)? Could Aristotle have been shorter, female, cleverer, his own twin? Is the River Thames rigid?