score:4
There are different approaches to explain the etymology of "αἰγαῖος πόντος / αἰγαῖον πέλαγος" (aigaios pontos / aigaion pelagos) as enumerated in the wikipedia entry on "Aegean Sea", e.g. αἶγες – aiges = "waves" and Αἰγεύς (Aigeús) as eponyms (see Ludi's comment above).
Gibbon (see note 13 in ch. 53) seems to offer an alternative explanation, based on the "similarity" between αἰγαῖος πόντος / αἰγαῖον πέλαγος and ἁγίος πόντος, thus "leading" to the medieval term archipelago(s) for the Aegean Sea. After a quick search, I wasn't able to find any other source for that etymological approach. Additionally, Gibbon's approach seems to presuppose the existence of orthodox monasteries around the Aegean sea, e.g. on Mount Athos, thus suggesting a specifically Christian connotation of "holiness", without roots in one of the antique cultures in Greece / Asia Minor. This isn't surprising since in the 53rd chapter, Gibbon writes about the 10th century CE. Maybe there are Byzantine sources for "holy sea", but I didn't know any. Google returns a myriad of hits where "holy sea" instead of "Holy See" is used (typos etc)...