Okay, it's not that common, but I know of at least 2 instances where someone with the given name Margaret has been called Daisy:
1) In 'Little Women' - this is more of an assumption than cold, hard fact, but Meg & John's daughter is called Daisy, and I assumed it was a nn for Margaret, after Meg. The other twin is named after John, and given the nn Demijohn, or Demi (little John).
2) I was just reading in the paper about this new diary that's been published, about an Australian schoolgirl sent away to finishing school by her stepmother. Her name was Margaret, but she was also called Daisy.
For the longest time, I thought Margaret meant Daisy, and have been very confused about this whole issue, ever since I found out that Margaret actually means "pearl".