His mate was Briavael.
A pack of gray wolves followed Taran and his Companions through the Eagle Mountains as they neared Medwyn's Valley. One wolf leapt onto Taran and kept him pinned as Medwyn appeared. Years later, Eilonwy later deduced that Brynach and Briavael had been among them. It's possible that Brynach had been the vary wolf who pinned Taran.
Brynach was overall loyal to his mate and good mannered to friends. As a wolf, he was also very fearsome in combat.