The story
Probably from ter(t-)b(utyl) + -yne + naph(thalene) + -ine.
Etymology from Wiktionary, CC BY-SA 4.0.
terbinafine
Today it means: A synthetic allylamine antifungal drug that is highly lipophilic, used in the form of its hydrochloride C₂₁H₂₅N·HCl orally in the treatment of onychomycosis and topically in the treatment of tinea corporis, tinea cruris, and athlete's foot. Full definition →