In Pete Seeger's collection _The Bells of Rhymney_ (Oak, 1964), the name is spelled Djankoye, and there is a photograph of the place with a sign spelling it Djankoy (also in Cyrillic letters, Dzhankoi). So the initial consonant should be pronounced like the English J. It is not clear why many people leave off the D -- perhaps to make it sound more foreign. As to the extra syllable at the end, perhaps that is the way it was in Yiddish.

Seeger gives a different etymology: "comes from two Tatar words, meaning 'Heart of Sheep'."