It seems to me this is a Greek borrowing from Hebrew because Latinized form of the Greek name ‘Αγνη (Hagne), derived from Greek ‘αγνος (hagnos) meaning "chaste" does not explain meaning.In Hebrew "HaGan et" (Hellenised es) means "The Garden [is] this", The Garden being The Garden of Eden, otherwise known as PaRDeS ('Paradise'). The meaning of "chaste" in Greek borrowing then becomes obvious because Eve did not conceive until after she and Adam were exiled from The Garden of Eden after the 'original sin', meaning in The Garden she was "chaste", i.e. a virgin, virginity being defined differently in the ancient Greek culture.
I think origin of this name is Lithuanian Agnė, Ugnė. This means fire in our language. In near pagan history of my country there was very widespread cult of fire, there is many girl names Agnė, Ugnė nowdays.