A cool way to look at the impetus behind rigid designators (the answer to the question you asked is at the end:)
"There is a natural and initially attractive conception of inquiry according to which ignorance about a given subject is a matter of lacking information about which, of certain relevantly different possible states the world could be in, it is actually in; and complete ignorance is a condition in which one doesn’t know which, of all the possible states that the world could be in, it is actually in. According to this conception, when an agent is in this condition, (i) all metaphysically possible states of the world are epistemically possible— i.e., every way that the world could possibly be is a way that, for all the agent knows, it might actually be, and (ii) every epistemic possibility is a metaphysical possibility— i.e., every way that, for all the agent knows, the world might be is a way that the world really could be. Inquiry is the process of escaping from this position of ignorance. By investigating the world or relying on the testimony of others, the agent learns contingent truths that distinguish the way the world actually is from other ways it might possibly be, but isn’t. Each time the agent learns one of these truths, he narrows down the class of metaphysical/ epistemic possibilities compatible with what he knows, and within which he locates the way the world actually is. According to this conception, acquiring information is equated with narrowing down the range of metaphysically possible world-states that are compatible with what one knows. We may also speak of the truth of one proposition as providing information supporting the truth of another. On this conception, the truth of a proposition p provides information supporting the truth of a proposition q by ruling out certain possible ways in which q might fail to be true. Thus, the truth of p supports the truth of q only if the set of possible world-states with respect to which both p and the negation of q are true is non-empty. There are two immediate consequences of this conception of inquiry. The first is that necessary truths are uninformative. Since they are true with respect to all possible world-states, knowledge of them provides no information, and is irrelevant to locating the way the world actually is within the range of possible ways it might be. Second, there are no necessary truths which, though knowable, are knowable only aposteriori. To say that a proposition q is knowable only aposteriori is to say that one can have the justification required to know q only if one has empirical evidence supporting its truth. However, according to the conception of inquiry just sketched, this is impossible. In order for the truth of anyproposition p to support the truth of q, and hence to provide evidence for it, there must be possible world-states with respect to which q is untrue, which are ruled out by the truth of p. Since q is necessary, there are no possible world-states with respect to which it is untrue; hence there can be no evidence for q. This means that, on the conception of inquiry just sketched, there can be no necessary truths which, though knowable, are knowable only aposteriori. Although a number of philosophers have taken this conception of inquiry, and the consequences that follow from it, to be plausible and even axiomatic, the conception is directly challenged by the frame-work developed by Kripke in Naming and Necessity. 1 This challenge is illustrated by the following examples. 1. Gregory Soames is not identical with (i.e., is not the same individual as) Brian Soames. 2. If Saul Kripke exists, then Saul Kripke is a human being. 3. This table is not made out of clay. 4. If this table exists, then this table is made of molecules. It seems evident that each of these sentences expresses a proposition that is knowable only aposteriori, on the basis of some sort of empirical evidence. In the case of (1), one needs to find out who Gregory and Brian are, and to assure oneself that they are different. In the case of (2), if the question were ever raised as to whether Kripke was a sophisticated robot, or an alien sent from another world, one would need empirical evidence to rule out these possibilities— though, of course, given their fanciful nature, not much evidence would be required. A similar point is true of (3), the justification of which might be provided by a cursory examination of the table. In the case of (4), the evidence required to know the truth that it expresses is much greater, and more sophisticated. Still, since in all four cases empirical evidence is required to know the truths expressed, all four propositions are knowable only aposteriori. They are also necessary. In each case, the subject expression is a rigid designator— the names Gregory Soames and Saul Kripke, plus the demonstrative phrase this table. 2 Because of this, the sentences express necessary truths iff the properties they attribute to the referents of their subjects are essential properties— the properties of being non-identical with Brian Soames, of being human, of being not made out of clay, and of being made of molecules. These do seem to be essential properties; in fact they seem to be essential properties of anything that has them. For example, it is plausible to think that any individual who really is not the same individual as Brian Soames could not have existed while being the very same individual as Brian Soames. Because the name Brian Soames is itself a rigid designator, we can also make the point in another way: since the property of being non-identical is an essential property of any pair of things that have it, if two individuals (such as my two sons) really are non-identical, then there is no possible circumstance in which they are one and the same individual. Similar points hold for the other properties mentioned in these examples— anything that really is human could not have existed without being human, any object not made out of clay could not have existed while being (originally and entirely) made out of clay, and anything that really is made up of molecules could not have existed without being made up of molecules. Thus, sentences (1– 4) all express necessary truths. Since they are also knowable only aposteriori, they are examples of the necessary aposteriori. How can this be? How can a proposition that is necessary (and known to be necessary) be knowable only aposteriori? Kripke’s answer appeals to our knowledge of which properties are essential. He argues, quite plausibly, that we know apriori that properties like non-identity, being human, being not made out of clay, and being made out of molecules are essential properties of the things that have them. So we know apriori that if things have these properties, then they have them necessarily."
Soames, Scott. Philosophical Analysis in the Twentieth Century, Volume 2: The Age of Meaning (p. 374). Princeton University Press. Kindle Edition.