By that time the island was inhabited by Phoenicians. Kadmos the son of Agenor, stopped at Kalliste during one of his wanderings in search of Europe. He left behind a group of Phoenicians who were accompanying him and among them was his kinsman Membliaros. These Phoenicians occupied the island until the arrival of Theras.
(Although the island was named after Theras, the name Thera -- without the final "s" -- is a female name which is usual for most of the Hellenic islands.)
Strogili means the "rounded". This name was given because of the round shape of the group of islands which form Santorini.
The name Santorini, which has a Latin root, was given by the Venetians who, after the Fourth Crusade (1204), had dominion over the islands. The origin of the name was the Chapel of Aghia Irini (Santa Irini - Santorini) which was built on Therasia. The Chapel was situated on a small bay where the Venetians moored their boats.