What should the study of infectious diseases in insects be called?
I suppose it depends on the level of specificity that you are looking for. Let’s start from the beginning. Pathology is the study of disease, illness, and its origins. In it’s most general sense, it would include all disease of any kind, including those affecting insects. There are sub-branches of pathology. Particularly veterninary pathology. A veterinarian treats non-human animals, so that would presumably also include insects, though I’d be surprised if a typical vet spent much time on such critters. Veterinary medicine has any number of sub-branches as well. The one specific to insects, as you have already pointed out, is entomology. So the study of disease specific to insects would most properly be called entomological pathology. Don’t get too excited, though. Having some passing familiarity with veterinary medicine in general, I can say that there is really not much work done even with dogs and cats (if I recall correctly, there are only two canine blood banks in the whole world)