Denali is only one of the native names its been known by, there were several others that pre date Denali, some of them by hundreds of years. Eskimos had various tribes or bands, each one had its own name, when you pick Denali you are recognizing one above all others, don't those other Eskimo groups have just as much right as the one that called it Denali.
Think about it as if Obummer came in and tells us he's renaming the Chickasaw National Recreation Area, changing it to Cherokee or Seminole or any one of the number of tribes in this state.
Other historical names for the same mountain
Former Gov Jay Hammond (died 2005) was the main guy wanting it to be renamed Denali.