Yup, as per
@beenherebeforeagain 's post.
Iceland was founded and named first, with it's name being a fairly unsubtle nod to the environment. But when Erik the Red was exiled (for murder or manslaughter, not sure) he travelled to Greenland and named the place hoping to encourage further settlers to follow him, and make the place more sustainable. They stuck to their traditional methods of farming, weirdly, and after some considerable time (many generations) the settlements starved out.
There are other theories about the name, though they strike me as less plausible. One is that the climate was milder then, which has been thoroughly debunked. Another is that the name was after the colour of the skin of the native Inuits, although that seems almost bizarre to me.
As for the OP...it seems a strangely Norse thing to have secular societies, with state churches.