I've always heard them called clan houses, but the ones up north are more square so...
I feel most qualified to talk about the Tlingit, but most of this applies to the Haida and I'm pretty sure the Tlingit as well. Inheritance of relics was an important part of Tlingit culture and were the property of the clan. These relics could be tangible (famous hats, clubs, and ceremonial regalia, for instance), intangible (heraldic designs, names, songs, dances, shamanic spirits), or somewhere in between (like usage rights to a particular patch of salal bushes or a particular salmon run). These relics could be traded in marriage or peace negotiations, including the non-tangible ones. Since Tlingit kinship was matrilineal, it was the clan matriarch who kept track of who had the current usage rights of these relics, especially names. (I can only say this specifically for the Tlingit, Haida, Eyak, Inuit, and Aleuts, but I believe it to be true for all of them: the names of the recently deceased could not be spoken aloud until the name had been passed to a new owner, and names were transferred to new owners--preferably direct descendants--as soon as possible. The name was believed to carry the soul with it. Names could also be given as gifts, and chiefly names were inherited when a new person filled the role so that they functioned both as names and as titles. An interesting aside, at least among the Tlingit, is that if one encountered another person with the same name, it was believed the two individuals shared the same soul and were to treat each other as relatives for the purposes of hospitality and the rights and obligations of kinship.) Anyway, I'm not certain how to represent that in game, but I think it would be interesting to give the Tlingit or Haida some bonus related to Relics.