In Danish, many exonyms are slowly dying. While next to no one uses Kalaallit Nunaat for Grønland (Greenland), Nuuk is always used nowadays instead of Godthåb.
From what I understand, the Greenlandic names are the official names now.
Slightly off-topic, but I guess we've already gone off-topic since we're talking about linguistics in general, and not just Rob Hatch's way of pronuncing things:
I will sometimes switch to 'Godhavn' when I completely fail at pronouncing 'Qeqertarsuaq'.