One of the theories about the village name origin assumes that the name derives from the river bed covered with white stone ("bily" means "white" in Ukrainian) and the word "oselya" (Ukrainian — the dwelling) or "oselyatysya" (Ukrainian — to settle down).

The folk tale tells about a father and 2 sons, one was blonde, the other one had dark hair. When they both got married, the blonde one inherited the land where Bili Oslavy located nowadays and the dark-haired one — the land where the neighboring village Chorni Oslavy was located ("chorny" means "black" in Ukrainian).

The other tale is about a district chief. Once he visited the villages behind the Prut river which were destroyed by fire. Right after passing Zarichchya he saw the village with white flowering trees. It was obvious that there was no big fire, unlike the neighboring village (Chorni Oslavy) where lots of woods were burnt. Compairing that, he said that these people have white (good) fame and that people have black (bad) fame.

There is also another story about merchants who delivered salt from Delyatyn long time ago. On the way to Kolomyja town, between modern Bili Oslavy and Chorny Potik villages, there was a dangerous place where travellers were attacked and plundered by robbers. That's why this place was called black (bad). There was also the other place (modern Bili Oslavy village), which was safe for travellers. That way it was called "white" (clean).