Named formal fallacies, like affirming the consequent, usually refer to inferences that can at least superficially be considered valid because they are often used as plausible inferences even when they are invalid (if smoke then fire, etc.). Denying modus ponens is not a mistake of this sort, so it has no name. And sometimes it is not a mistake at all, it is done to make a point that the meaning of terms, implication in this case, depends on the rules we adopt for manipulating them, like modus ponens. Someone may reject modus ponens because they decline to use classical implication, and prefer some alternative logic. Modus ponens fails in Lukasiewicz's 3-valued logic, for example, but this is rare.
Denial of modus ponens was featured prominently in Lewis Carroll's dialogue What the Tortoise Said to Achilles. The argument discussed is:
A: Things that are equal to the same are equal to each other
B: The two sides of this triangle are things that are equal to the same
Z: The two sides of this triangle are equal to each other.
The Tortoise points out to Achilles that one may accept that A and B are true, but not yet that if A and B are true then Z true. Achilles concurs. Then Tortoise agrees to accept
C: If A and B are true then Z is true;
but points out that one can similarly accept A, B and C but not conclude Z. Why? Because she says this needs yet another premise "If A and B and C are true then Z is true", and so on.
The infinite regress comes from the fact that application of a principle, here modus ponens, is different from declaring it, and in effect one application compresses infinitely many declarations. As Wittgenstein put it, "there has to be a way to grasp a rule which is not an interpretation". The Tortoise attempts to replace such practical grasping with endless interpretations, and effectively ends up rejecting modus ponens as a result. She asks for modus ponens to be substantiated before it is applied, instead of taking it on faith, and it turns out that it can not be so substantiated. If the Tortoise fails to grasp the rule there is nothing that can make it do so. Achilles can not make the Tortoise apply modus ponens by simply getting her to accept declarations. Even logic requires something extra-logical.