Assessment of Kripke's attack of reference-fixing descriptivism

How is it that when someone speaks a name, we understand who they are speaking about? When someone introduces a new name to us, how do we know what object is satisfied by the conditions with which the name is associated? Reference-fixing descriptivism suggests that a name refers to an object because the name is associated with a definite description, and that definite description refers to the object.
Frege was a descriptivist. He acknowledged that there are some difficulties in cognitive values between certain cases, such as the Hesperus/ Phosphorus case. He explained this cognitive difference by stating that names express the sense of an object, which presents the object that the name refers to. Therefore, the sense of the object that a name expresses determines the object that the name refers to. Thus, speakers can have different senses that present the same object.
Frege believed that his theory of sense and reference can be used for proper names of people as well. Frege uses an example a name of ‘Aristotle,’ where there can be different senses associated with the name 'Aristotle.’ For instance, I can associate the name ‘Aristotle’ with the sense of the philosopher from Stagira, who studied philosophy under Plato. Someone else can associate the name ‘Aristotle’ with the sense of the philosopher who taught Alexander the Great. These are both definite descriptions that act as different senses of the object Aristotle. In short, Frege’s theory on reference-fixing descriptivism suggests that if n refers to o, it is because n is associated with the definite description The F and The F refers to o. Frege explains that our language is imperfect and therefore there can be different senses for the same object.
Kripke finds a problem with reference-fixing descriptivism. What if the sense of the object that is expressed by the name is associated with conditions that are not actually satisfied by the object? Kripke uses the example of Gödel, who developed the incompleteness theorem. Kripke asks that we imagine a philosophical experiment in which Gödel is not the discoverer of the incompleteness theorem. In our thought experiment, Schmidt is the actual discoverer of the incompleteness theorem, but Gödel steals the idea from Schmidt and then Schmidt dies a mysterious death. Gödel then claims that he discovered the incompleteness theorem and nobody knows that poor Schmidt is the true discoverer of the incompleteness theorem. Gödel is associated with the definite description ‘The person who discovered the incompleteness theorem’ (x). But (x) is also associated with Schmidt, the person who actually did discover the incompleteness theorem. Kripke identifies that reference-fixing descriptivism suggests that if n refers to o, it is because n is associated with the definite description The F and The F refers to o. However, the problem presented contradicts the theory because, in the example, Gödel is associated with the definite description the discoverer of the incompleteness theorem, which is false. This suggests that there is a conflict between theory and data.
Kripke makes a good argument, but Frege could have replied to this attack. In the example, the name is simply being attached to the wrong definite description (or the wrong sense). Gödel should be associated with the definite description, the person who most people believe is the discoverer of the incompleteness theorem. In this case, the name Gödel refers to the object (the man who is called Gödel) because the definite description would accurately be associated with the appropriate object, the man who is called Gödel.
Frege might also argue that there are many definite descriptions (or many senses) that can be associated with a name. The reference of a name to an object is not solely dependent on one definite description. The sum of all of the true definite descriptions is the conditions that may be satisfied by the object, which should be associated with the name. Just because there is one wrong definite description that a name refers to does not mean that there are many other definite descriptions for that name that would pick out the appropriate object.
Kripke’s response to this defence would be that Frege is making a false assumption in his analysis. Both of Frege’s claims are circular propositions. If Frege’s argument is that Gödel is being associated with the wrong definite description, and the solution it is to change the definite description so that it refers to the appropriate object that satisfies the conditions, Frege would be presupposing that Gödel refers to the man who is called Gödel. Reference-fixing descriptivism is supposed to supply an answer as to why a name is associated with an object; moreover, why Gödel refers to Gödel. Similarly, if Frege claims that there are many other definite descriptions that will pick out the appropriate object, he is presupposing that we know that Gödel refers to the man who is called Gödel. So, the response supplies a theory as to why Gödel refers to Gödel, but it requires that we already know that the name Gödel refers to the man called Gödel. Kripke would note that the claims violate the condition of circularity, and thus Kripke’s counterexample is valid.