I must confess that I liked FauxLivia (BoLivia, whatever) a LOT better than our universe's Livia. She was so much more alive and fun!
I called her "Otherlivia," but it never caught on.
And yes, Fauxlivia was great fun. One thing I liked about Anna Torv right off the bat was her warm smile, but over time, Olivia got so much more somber and closed off. Fauxlivia was a breath of fresh air. And Torv's transformations were amazing. In the first half of season three, she was playing four distinct characters -- Olivia, Fauxlivia, Fauxlivia impersonating Olivia, and Olivia brainwashed into thinking she was Fauxlivia -- and making them all clearly distinct from one another. Like I said, it was the same sort of thing Tatiana Maslany does in
Orphan Black, and Torv did it just as well.