Perigune, the daughter of Sinis and Sylea, was the mistress of Theseus, to whom she bore Melanippus. Her name, which is composed of the elements peri, 'round' and gounos, 'fruitful land', can be interpreted in two ways.
Either it is a purely propitious name, bringing wealth and fruitfulness, or it refers to the episode where Perigune fled from Theseus, hid in the vegetable garden, and begged the plants there to rescue her. So either 'fruitful land all round' or 'round the vegetable garden'.