If I liked Daisy or Sasha or Sadie enough to want to use them at all, I'd just give them as the full name. I would think that somebody who names their daughter Margaret and then calls her Daisy is being unbearably "oh, see all the books we have read! We gave this fine, dignified name Margaret after dear Great Aunt Meg, but we shall call her Daisy! It's in all the books we have read! By the by, did you know we have read many books!"