Sorry, it's a Scots/English nicknaming habit - terribly important here, nicknames show love, affection, acceptance and were traditionally used by your inner circle of friends and family. My husband (5'4", former runner, rugby winger and Formula 1 driver) was dubbed 'Mini' for the Mini car - small but fast, get it? LOL He's nearing 50 and still called 'Min' by everyone we know intimately. I call him 'M' because he'd slowed down by the time I met him ;o)
You have Margaret but she's a wee thing and the name's too big. So you start playing with sounds and letters. So there's Maggie then Meggie then Meg. Or there's Margie and Margarie and Margerie and stew it a while and you get Marjorie. And since in Scots Gaelic Margaret is Maighread you get Maighrie and Maisie and Maisy and whoa, hold up, Daisy!
Margaret was in use as an northern qqqqqEnglish dialect word for the daisy even before the French adopted Marguerite in the 19th C. to refer to the large, cultivated variety of daisy. The French equivalent, Marguerite, was imported into English just in time to catch that turn-of-the-century (late 1800's, early 1900's) vogue for girls named for flowers.
So Daisy was a pun, from the English margaret daisy and the French marguerite daisy and the similarity with traditional Scottish/northern English nn Maisie for Margaret. And in the late 1800's it became a 'cute' way to honour a relative named Margaret without repeating the name which seems to have a love/hate response in the general public.