I received today cuttings of a variety from Russia, called Uzbek Blue (Узбекский синий)
It seems from the Internet that it is grown in Russia, Ukraine and Belarus.

I find this description :
Узбекский синий. Соплодия грушевидной Формы, ребристые, крупные. Окраска сине-фиолетовая, при созревании плод растрескивается. Мякоть коричневого цвета. Плодоносит дважды в год. Плоды сладкие с нежной кислинкой. Деревце выглядит очень нарядно.
Automatic English translation : The Uzbek blue. Pear-shaped stems, ribbed, large. The color is blue-violet, when ripe, the fruit crackles. Flesh is brown. Fruits twice a year. Fruits are sweet with a tender sourness. The tree looks very smart.

Does anyone grow this variety or now about it ?

(this website shows figs from Uzbekistan, among which a blue one : maybe the same ? http://www.centralasia-travel.com/ru/countries/uzbekistan/natural_blessings/fig )