A challenge and query re rigid designators
Rigid designators are about the criticism of the theory of descriptions. "Aristotle is the author of Metaphysics" is contingent. Aristotle could not have written Metaphysics. This implies that descriptions might not be the contents of names. "Aristotle is Aristotle" is necessary. Aristotle could not have failed to be Aristotle himself. This implies that the contents of names are the referents themselves.
The title of the book written by Kripke is 'Naming and Necessity'. It's about naming and necessity. Suppose that I name someone as 'Fred'. Then, subsequent uses of the name by me continuously refer to the same person in every possible world. The first is naming, and the second is necessity.