My chapter did families, but we never named them. I can count my family back 11 generations. It's pretty neat to now follow all of those women on FB and see how they turned out to be professional women with ties to AOII. I love it. I perpetuates the lifetime aspect of the organization. I don't understand the family name since over time that may or may not mean anything to the people in the family (imagine a name picked by people in the 70s being relevent to members now.
) It's all up to what your chapter want to do, though.