It does get overplayed though, with people acting like there was no reason to name Iceland "Ísland" and no reason to name Greenland "Grænland". There's plenty of ice here (much of the middle of the country doesn't melt until quite late in the year, and settlers approaching from the south and east sailed past the huge terminal glaciers of Vatnajökull), and the places that were settled in Greenland weren't all that different from e.g. Vestfir(th)ir. Grænland was chosen as a name to advertise it, but it's not like it was some sort of lie - most new settlements, even random villages wherever you are, are generally given pleasing names to try to attract people.
Also, Iceland got its name due to Flóki "Raven" Vilgerðarson, the viking-discoverer of Iceland (though the Irish already knew of Iceland). He had a clever trick to find islands, which was having ravens (land birds) on his boat; they'd fly up, look for land, and if they spotted it, beeline for it, but otherwise had no choice but to return to the boat. Ravens are quite large, black birds and thus easily visible to track from a boat. Anyway, his first winter at Bar(th)arströnd was abnormally cold, and there was sea ice visible offshore (something quite rare in Iceland), so he chose the name "Ísland".