Sorry, you had to ask twice, and I am not the one to answer, I just didn't want to ignore your question. But I would guess that no one chooses the names and that it would be based on the most powerful/richest family (or 5 most powerful). Possibly the ones with the most "control." Each family of course having a "Head Don", thus getting the family name. Am I close experts????
"Mankind must put an end to war before war puts an end to mankind. War will exist until that distant day when the conscientious objector enjoys the same reputation and prestige that the warrior does today." JFK
But I would guess that no one chooses the names and that it would be based on the most powerful/richest family (or 5 most powerful). Possibly the ones with the most "control." Each family of course having a "Head Don", thus getting the family name. Am I close experts???? 
