https://en.wiktionary.org/wiki/%D0%B3%D1%8D%D0%BA%D0%B0%D0%B...
https://en.wikipedia.org/wiki/Southern_Russian_dialects
https://ru.wikipedia.org/wiki/%D0%9D%D0%B0%D1%80%D0%B5%D1%87...
There's so much no such sound that I've seen Hebrew and Arabic transcribed into Russian with the character "h" for that sound.
> Does this phenomenon have some name, as googling didn't turn out much?
Certainly not a formal one. Хэканье? Or maybe simply украинский акцент?
It should be noted that even in Russian, /ɣ/ used to be the more common pronunciation throughout the Empire until the end of the 19th century or so, due to the influence of Church Slavonic (in which it is also /ɣ/). And it's still preserved in modern standard Russian in some words, such as бог (god) - /boɣ/.