I think it is important to know the meaning of these names... you probably know that.
If you look into A.Beider's Encyclopedia you find the surnames (this is how the names were pronounced.. not real spelling):
KHAMUDIS was popular in Kishinev, Bendery, Akkerman and Taurida (Crimea)
KHAMUDES was popluar in Minsk and Soroki
KHOMUDIS was popular in Akkerman
and the surname LEBEDINSIKIY was popular in many places mostly what is now Ukraine.
All the best,