Ah yes arguments about Iceland being icey or not, this was inevitable. Yet we have to understand the first nordic settler (Viking settlers as most people know them as.)
Settled in Iceland during the spring, they arrived in the spring however and had not given this new country a name yet. Hrafna-Flóki (as he was called for having 3 ravens fly to find him land to settle upon) was the first settler on Iceland and settled in Vatnsfjörður, Vatnsfjörður was a place where there was plentyful of fish for the settlers, but the settlers being so pre-occupied fishing rather than preparing the livestock that they arrived with for the winter. Thus when winter arrived the lifestock died and forced the settlers to leave Iceland, but before leaving Hrafna-Flóki hiked up on a mountain and looked down only to see the land covered in snow and ice. (Obviously discouraging people to live there due to waste of manpower, resources, etc) And therefore the name: Iceland stuck to it. But there were two other names for the country. One seafarer called Naddoddur Ástvaldsson from Norway. Named the land "Snæland" or "Snowland". Another seafarer called Garðar Svavarsson a viking from sweden. He named the land "Garðarshólmur" "Isle of Garðar". But after Hrafna-Flóki left Iceland only to come back there and become one of the permanent settlers.
"Greenland" has two explanations, neither of which is verifiable. The place was named by Erik the Red when he discovered it in the year 982.

One story says that his family was from Grønland, a town in Norway, and the name comes from that. That happens alot, people naming a place after the place they came from: New York, New England, New Brunswick, Nova Scotia. etc.

Another story says that he simply called it that to make it sound nice (even though it is very cold and harsh) to attract settlers.

(I had to dive into this a bit to find some new information about this because I only remembered the part where he looked upon the land in the winter and a couple of more blurry things.)
Correct me if I am wrong.
This is just a longer version of "Iceland was named Iceland to prevent settlers from arriving there and Greenland was to attract settlers."