Not exactly named after a drug but I know of an ID pharmacist who named his dog Alcaligenes xylosoxidans, Xylo for short. Although xylosoxidans is in the Achromobacter genus now so the name is a bit dated.
Pharmacy already takes up more of my life than I'd like so I don't really get the urge to name a pet something pharmacy related. But you do you I guess.