The Borg knew about the Feeration even earlier than that, when they assimilated Magnus, Irene, and Annika Hansen in 2356..
You're thinking of Erin
Hansen. Irene Hansen was Seven's aunt, and she was never assimilated.
I recall the Borg wanting to add a species' biological and technological distinctiveness to their own, but nothing about their culture.
It's like a real-world country welcoming immigrants (biology) and their intellectual know-how and "stuff" (technology), but saying "Forget about your former culture, you'll have to adapt to ours."