PARIS—French luxury-goods house Hermès International named Nadège Vanhee-Cybulski as its new women’s fashion designer on Thursday, betting on an unknown name who will be dedicated to the house full-time.

Ms. Vanhee-Cybulski will begin by designing the fall-winter collection after the departure of the current designer, Christophe Lemaire, in October. Earlier this week, Hermès announced the resignation of Mr. Lemaire to focus on his…