Honest good-faith question: do Alberta, Yukon, NW Territory and Nunavut indigeonous people actually take issue with the name, or is it mostly white liberals? I genuinely don't really know and this is a serious question.
By and large they self-refer as Inuit and not as Eskimo. They generally don't care for the term Esquimaux. Whether they object to having a sports team named after them, I have nary an idea, but Edmonton Inuit would lose the alliteration, so if Edmonton does change the name, I can't see them switching to that.