@feelingverylazytoday
Bettybuttons perhaps in mumsnet land. In real life it's an actual name, because people don't pick a name they don't really like, then arrive at another name by word association and call it a nickname. They just choose the name they like in the first place.
Here's a clue, OP. Nearly every post has suggested a nickname (s), that suggests that nobody really likes the name 'Margaret'.
Nowadays if new parents want to call their child Daisy, they will probably put Daisy on the birth certificate. Until a few decades ago, they probably wouldn't have done. Registrars, priests/vicars/ministers etc, older family members, society generally said there should be a formal name on the birth certificate. You could call your child what you wanted at home, but on her birth certificate and baptismal records you'd see the formal version, which for Daisy would be Margaret, as so many people have explained.
This is why birth records from generations ago are full of names like John, Joseph, Robert, Henry, Mary, Margaret, Katherine, Elizabeth and so on but if you'd met most of those people they'd have been introduced as Jack, Joe, Bob, Harry, Polly, Maggie, Kate, Lizzie.
Even now, some of us still prefer to do that, as it gives the child a choice as they grow up whether to use the full name or a shorter version/nickname. I suppose there's no reason, though, why a child shouldn't do the reverse of the old approach - Joe on birth certificate, asks to be called Joseph, for example.