Here is a list of variations on this last name with current profile counts on Geni.com;
Boboyev 4 Babaiov 3 Babaeff 21 Babaev 270 Babaioff 171 Babayoff 130 Babayev 477
Variations of this last name are due to the phonetic equivalents in their respective host countries.
There are at least 3 distinct family lines among Jews carrying this last name. They can be Cohanim, Leviim or Israelim.