They seem to be accompanied by commentary like "son of" or "the fisherman", or nicknames that apply to individuals. Dumuzid "the shepherd", 36,000 years. Kug-Bau, "the woman tavern-keeper, who made firm the foundations of Kish" reigned for 100 years, which is just possible but pretty good going. You have to wonder at what point in her ~120 year life she did her tavern-keeping. Perhaps while ruling?

So, OK, maybe it really means "Kug-Bau, the woman tavern-keeper, and her descendents, not mentioned here".