Being a neighbour of Greenland, as well as probably the only one on this thread to have actually been there, I will give to you the most commonly accepted explanation of the name.
The discovery of Greenland took place in the 10th century, and the explorer was Eric the Red, - a Norseman who had (due to trouble) settled in Iceland, then again, (trouble) explored westwards and came across some nice valleys to farm, - on the west coast. He crossed the cape and went further, - I have only been ineastern Greenland.
Anyway, his son then went on to exploer some odd part of the USA/Canada. (Leif the lucky, or Leifur Eiríksson)
Back then, there was this lovely spark of GW,not MMGW. So Greenland back there, as well as Iceland, were even friendlier than today.
The name is belived to be the first big ad-hoax in world's history, since it was after all, a big continent being mostly a mountanious glacial area, and NOT big green grazing grounds. However, Due to the green hillsides in contrast with blue sea and white icebergs, the landscape really gives you a green image....in certain /sailing) times of the year.
BTW the Greenland glacier is very much older.....than civilization.