I think of Unity Mitford but it's not an overwhelming association, if I met a Unity I'd get over it. I can see the appeal but it seems more like a slogan than a name to me - I can't imagine calling out for Unity.
Ha - I know what you mean about it seeming more like a slogan. I'm trying to find more U names that I like - Una and Ursula are unusable as my surname begins with an A and they run into together too much.