The Wikipedia entry for the place gves a slightly different etymology from what I thought, though still a Turkic one: Dzhankoy. That northern Tatar word for "new" (which I don't know how to encode in HTML) must be a cognate of standard Turkish "yeni".

The Wikipedia entry has rather few historical facts, but says Canköy/Dzhankoy got city status in 1926. This article http://www.euronet.nl/users/sota/ctnm.htm dates that as one of the last acts of the autonomous Crimean Soviet government before Stalin clamped down on it.

This gives a concise description of the final deportation: Otto Pohl's blog.

It is just not believable that the Jewish settlers of around 1930 were reclaiming vacant land. The whole of the Crimea has been settled by agriculturists for thousands of years. Somebody had to have been displaced first before the people in the song could start farming.