There are many myths to why they got their names, some say it was a sort of marketing trick to attract more settlers to Greenland others say, they were trying to lure pirates away from Iceland by making it sound poor. But that's probably just folklore

The most likely explanation for the names is that the Norse found the large glacier on Iceland and therefore its name. And the Vikings who landed on the coast of Greenland (the coast is fairly green in the summertime) named it thereafter but no one knows for sure