The island was named after Saint Eustratius (Όσιος Ευστράτιος ο Θαυματουργός), who lived on the island in the 9th century as an exile, because he was opposed to the iconoclastic policies of the Byzantine Emperor Leo the Armenian.
A illa leva o nome de San Eustaquio (Όσιος Ευστράτιος ο Θαυματουργός), que viviu como exiliado na illa no século IX, porque se opoñía ás políticas iconoclastas do emperador bizantino León V o Armenio.