Denali is not a religious word, it means “the high one” or “the great one” as in highest or greatest mountain.
"Also known as Mount McKinley, this peak is the highest peak in North America and holds great significance within the native traditions. "Denali" is translated as "the great one" in the Athabaskan languages of the Alaska Natives living around the mountain. The mountain is part of the Tena creation myth, serving to block a spear thrown by the demi-god Yako's rival Totson."
Source:http://www.huffingtonpost.com/2014/05/29/most-spiritual-places-america_n_5360618.html
The mountain's name means "great one" or "high one", but in the context of being a sacred place in the Athabaskan Indian tribal religions.
Indeed, reference is made is some articles about the name change that deference to sacred traditions of these Indian tribes is a factor in the name change.