http://vkontakte.ru/id14645393http://vkontakte.ru/id14645393 a young guy from Koidanava (Dziarzhinsk), who's name is Max Bakovski. He is likely to be related to you, since Bakinovskij iz not the most common surname.
I understnad that you would need to register an account there to send messages to these groups or people. The account is free, but unlike facebook, they have recently introduced a mandatory invitation procedure. I have an account there and can (try to)send you an invite. For that however, I will need your mobile number, where an automatic message will be send by the website.
I understand this is kind of spooky. In no way I am myself associated to the website (except an account there) and I will not in any way benefit from sending you the invite.
In case you are on facebook, https://www.facebook.com/profile.php?id=100002528716606 is Vika Bakinovskaya. As far as I can tell her account on vkontakte is http://vkontakte.ru/id110786854http://vkontakte.ru/id110786854 and she is friends with the Max guy above (sister?) so has to be from Koidanava too.
No idea about orphanages. As to surnames related to village names, it is not uncommon for both peazants and nobility.
Sorry if I can't be of much help. Since I am not in Belarus my searrch capabilites are pretty much limited to whatever is available online.