The Just-So story of antiquity is as Konstantinos Konstantinides put it: Thera the island was named for its colonist Theras, and Therasia for his daughter.
Yeah, I find that too convenient too.
I’m not looking up Pauly or anything reputable like that, but I will work from the corresponding common nouns. Thēr means a wild animal, and thēra meant the hunt, hunting for wild animals, game. Thērasios is the adjective of thēra, “of or relating to the hunt”. The feminine of Thērasios is Thērasia. So “hunt” and “hunting (island)”.
Oh, and Theresa does indeed come from the similar adjective Thēresios. It started out as a synonym of Artemis, the hunter goddess.