This has already been answered by @sumwun but I have some details I would like to share.
The name may have been deprived from the school known as Kōga-ryū from a Japanese legend. It's a school that teaches Ninjitsu, in which the students (Shinobi) are trained in disguise, escape, concealment, explosives, medicines and poison; moreover, they are experts in techniques of unarmed combat (Taijutsu) and in the use of various weapons.
The use of Poison and Medicine may refer to Koga, Gekkouga may be Dark due to Disguise, escape and concealment, while everything in general refers to both.
Also, there was a time when had read the whole Bulbapedia article of scrapped features and such (don't judge me) and never had heard of Poison being strong against Psychic. (edit: I can't find the page, I was probably thinking of something else.)