It's actually the source of some very bad blood in some circles. Apparently the issue even shows up in the campaigns of some Ohio senatorial candidates, who pledge to keep the mountain named "McKinley."
Not surprisingly, many Alaska Natives see this as a personal affront. It was "Denali" a long time before it was McKinley.
From Athabascan, translates as "the great one" or "the high one." This is the Athabascan name for Mt. McKinley, the tallest peak in North America. Everyone in Alaska refers to Mt. McKinley as Denali and the name of the national park surrounding it was changed to Denali National Park to reflect this. Alaskans routinely attempt to have the name of the mountain changed to Denali (it's "officially" Mt. McKinley, according to the US Board of Geographic Names) but this attempt is blocked each year in the US Congress by senators from Ohio, President McKinley's home state.