At the nearby village Inachorio there was a sanctuary of Ina, where ceremonies were held to consecrate the seas. Ina was cursed by Hera (Zeu’s wife) to lose her brain, because she helped Zeus keep a secret about loving another woman.
Elafonisi is located in western Crete about 75 km southwest of Chania. It has an area of 0.435 km (Wikipedia) and a maximum altitude of 30 meters. We would say that it is an island but also a peninsula, depending on the years tide, you can walk to it.
The story of Elafonisi goes back in the depths of centuries, since there was a shrine dedicated to the Apollo Mussagore. Musaeget means leader of the Muses, a nickname given by Pindar to Apollo. It refers to the Muses who sang around the Hippocrine spring. The 9 Muses, mocked the sea deities with their music.
As a result Ina suicided after she and her husband killed her own son after saw a hallucination of him as a deer (=elafi in greek). Then her body and her son’s body lost into the sea near the island which is named elafonisi.
That’s in among others one version of the story.