No, Dagny is not a family name. However, I have discovered (1) many Grandmothers from ladies on my due date forum named Dagny, and (2) that some folks pronounce it "Downy" instead of "Dagnee".
Dagny Taggart is the heroine of "Atlas Shrugged" by Ayn Rand. I first read this book while I was in professional school and thought it was amazing and spooky at the same time. I pestered Doug to read it, but he was reluctant. Years later, he bought himself the tapes (abridged version) and listened to it while driving to and from work - voila, a changed man. Always a capitalist and a "producer" type of person, Doug adored the book and downloaded the unabridged version onto his i-pod as his first Audible selection. Now he listens again every few months to avoid being sucked in by the "looters". [Gotta love Audible.com and the i-pod when commuting from Roswell to Dacula!]
Annika is not a family name either. We found it because of the golfer, Annika Sorenstam, but did not name Annika after her. Annika was actually Lydia for about 3 hours until I had a hormone moment in the hospital after Doug fell asleep and changed it to Annika.
Oh, and Doug wanted our girls to have tough names so that it would be appropriate for a neighbor to call us to say that "Annika" or "Dagny" beat up his little boy at the bus stop. Lydia and my other girly name choices just didn't work. Svetlana would have been good but it seemed a bit over the top.