Margaret may have sounded heavy to danish ears back then, but remember that foreign names often changed from country to country, especially when it comes to royalty. Margaret was changed into the swedish form; Margereta, when she married, and the danish version of that name is Margrethe. And when you look at her name, you can see that she bear the names of three of her female predecessors (Thorhildur was to show the ties between Denmark and our atlantic possesions, Iceland, Greenland and the Faroe Islands), so she would probably have been named Margrethe, no matter what the medieval queen's name had been.
A little sidetrack: The Prince Consort is named Henri, but it was changed into the more danish Henrik, when he married Daisy. Just like the english kings, James and Charles are known in Denmark as Jakob and Karl. And the danish viking King, Knud, who conquered England, are called Canute in English history books. It's only recently we stopped changing names into more their more "danish-like" version. When Frederik was to wed Mary, there was a huge debate in the public if she should change her name into Marie. It was especially the elder part of the population, who wanted this name change. (Many of them pronounce her name in the heavy and somewhat flat danish way; "Mar-y", instead of the english way "Mari". Personally I think it's some kind of protest, because her name was'nt changed into Marie. Some elders can be so stubborn!

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But of course it was a popular and very patriotic choice of name, because many was put in mind of the great queen, especially considering that she was born a week after the german occupation. And it certainly touched the national pride. When her father died, there was grand discussion of wether she should be Margrethe I or Margrethe II, considering that medieval Margrethe first was queen of Norway, and only later became queen of Denmark as well. But that was settled once and for all when the prime minister, from the balcony of Amalienborg, officially announced the death of King Frederik IX and proclamed his eldest daugther Queen Margrethe II of Denmark.
Queen Ingrid once said that Margrethe was called Daisy from the very beginning by both her and her husband. And the famous Marguerit/Daisy jewellry was made in connection with her birth. (BTW, they have become very popular again right now, so the prices, after being quite moderate for a generation or so, have gone through the roof lately) So I guess it's only natural that Daisy always have felt something special for this particular flower.
