In Six Ages: Ride Like The Wind your clan is divided into seven families, a system attributed to Relandar's wise ranking and division of people during the exodus. Each family is composed of nobles, commoners, and elders who rule on disputes.
It's best to have one representative of each family on your Clan Circle, as circle members defend their families' interests and bring their relatives' concerns to the council. Naturally, unrepresented families are likely to complain about the matter.
Of your heroes, Yatakan, Ayvtu, and Beren the Tall seem always to come of different families. It isn't known if the same is true of the Former Wheel.
The possible family names are Akot, Dasano, Erkent, Karent, Nordon, Parnt, Turent, and and Zarent. One name goes unused in each game.
Your starting chieftain will always be a member of either the Akot family or (if the name Akot is unused in this game) the Dasano family.
By the time of Lights Going Out, the importance of families to the political ruling of your clan has diminished since becoming part of a tribal kingdom. Families still exist inside the clan, but they are no longer important in balancing the ring and they are not visible when selecting leaders.