An island that is about 81 percent ice sheet was named by a man looking for recruits.
According to the Icelandic sagas, Erik the Red was an outlaw. The Saga of Erik the Red says a feud over a landslide led to his banishment, first from his district and then from Iceland. Wikipedia's history of Greenland puts his exile at around 982 and says it was for killings, with a term of three years.
Erik spent his exile sailing west to a land that others had reported seeing. He explored its coast and found habitable ground in the south. Then he went back to Iceland to find settlers.
The sagas say he chose the name with that goal in mind. In the translation Wikipedia quotes, he called it Greenland because people would be attracted there if it had a favourable name. The Saga of Erik the Red, probably written down in the 13th century, tells the story the same way: an attractive name to draw colonists.
The pitch worked, at least at first. The sagas say 25 ships left Iceland with Erik in 985, and 14 arrived. The Norse built an Eastern Settlement and a smaller Western Settlement. Radiocarbon dating suggests settlement began a little later than the sagas say, around the year 1000.
The name was not a pure lie. Visit Greenland describes what Erik found in the south as inviting fjords and fertile green valleys. Ice cores also show a milder period from roughly 800 to 1200. After that the climate cooled. The last written record of the Norse Greenlanders is a wedding at Hvalsey Church in 1408, and the settlements were gone by the mid-15th century.
The Norse habit of plain descriptive names shows up across the North Atlantic. Iceland is said to be named for a fjord full of drift ice. In the Saga of the Greenlanders, Erik's son Leif names Helluland for its flat stones and Markland for its forests.
Greenland's own people use a different name. In Greenlandic it is Kalaallit Nunaat, "land of the Kalaallit," the main Inuit group of the west coast.