Although Ionia (in Asia Minor) is named after Ion, son of Apollo and ‘father’ of the Ionian people, the Ionian Sea and Ionian Islands are named after lovely priestess Io, who caught the eye of Zeus. When the jealous Hera was about to catch the couple in flagrante delicto, Zeus changed Io into a white cow, but Hera was not to be fooled. She asked Zeus to give her the cow as a present, and ordered the sleepless hundred-eyed Argus to watch over her.
When Hermes charmed Argus to sleep and killed him, Io the cow escaped, only to be pursued by a stinging gadfly sent by Hera. The first place the hapless cow fled to was named after her: the Ionian Sea.
Image by Bibi Saint-Pol, Creative Commons License