Astromycology was the study of alien fungi. A scientist who specialized in the field of astromycology was known as an astromycologist. (DIS: "Context Is for Kings")
Paul Stamets was an astromycologist. After seeing his presumed dead partner, Hugh Culber, in the mycelial network he studied, he started wondering if it could be more than a mental fabrication, because astromycology has taught him that nothing is ever truly gone. (DIS: "New Eden")
At one point, Saru complimented Sylvia Tilly on her comprehension of the astromycology behind Stamets' findings. (DIS: "The Wolf Inside")
Mycology is the study of fungi, while astro- (like exo- and xeno-) is often used both in real life and in Star Trek to indicate a the part of a field looking at extraterrestrial examples. For example, astromycology is presumably a subfield of astrobiology.