Interesting point! I came across this problem of how to adress the people in East Greenland, who generally call themselves "Ivii" (- which means "the people" in East Greenlandic, a non-written Inuktituk language). From my experience, East Greenlanders neither like being called "Eskimo" nor "Inuit", the latter being the West Greenlandic term for "Ivii" (West Greenlandic is the official language in the Easten part of the country and is being used for written texts as well as for school education). On the other hand, most of the time people in East Greenland rather relate to a national identity than to an ethnic identity and call themselves "East Greenlanders". This also seems to be a widely accepted term when speaking about them. However, the issue on contrasting identities (i.e. national vs ethnic, as a very basic one) is a quite complex subject.
I agree with Steve Sailer and find it very useful to reflect upon our wide-spread manner of trying to use "the local names" of ethnic groups that on the other side don't take over our supposedly more than correct attitude...