Another factor is the lack of the h sound in the Russian language; there is no letter to represent this sound in the Cyrillic (Russian) alphabet.  Foreign words (such as Jewish names) containing the h sound were spelled using either the hard g sound or gutteral kh sound instead.

Thus names like "Hirsh" and "Hinda" became "Girsh" and "Ginda", or "Khersh" and "Khinda".  In some Lithuanian and Ukrainian regions, the initial h sound tended to be dropped entirely, so "Hirsh" became "Irsh", and "Hinda" might appear as "Inda".