The Hansen family was the family of Annika Hansen, later known after her assimilation by the Borg as "Seven of Nine".
Annika was the only child of her parents, named Magnus and Erin. Her father had at least one sister living on Earth, Irene. (VOY: "The Raven", "Dark Frontier", "Author, Author")
The bio-plasmic organism encountered by USS Voyager in 2375 showed another supposed aunt of Annika, named Claudia, but she turned out to be a fictional creation. (VOY: "Bliss")
In the 22nd century, one of the ancestors of the Hansens was Sven "Buttercup" Hansen, a boxer. (VOY: "11:59")