Edit:

Yes sorry, Tahoma and Denali were names that came first before politicians decide to use these names like unearned rewards who have no real connection to the mountain.

>Mount Rainier was first known by the local Salishan speakers as Talol, Tacoma, or Tahoma. One hypothesis of the word origin is təqʷubəʔ 'mother of waters' in the Lushootseed language spoken by the Puyallup people.[15][5] The linguist William Bright gives the origin as təqʷúbə 'snow-covered mountain'.[16] Another hypothesis is that Tacoma means "larger than Mount Baker" in Lushootseed: Ta 'larger', plus Koma (Kulshan), (Mount Baker).[17] Other names originally used include Tahoma, Tacobeh, and Pooskaus.[18]

>The current name was given by George Vancouver, who named it in honor of his friend, Rear Admiral Peter Rainier.[19] The map of the Lewis and Clark expedition of 1804–1806 refers to it as "Mt. Regniere". Although Rainier had been considered the official name of the mountain, Theodore Winthrop, in his posthumously published 1862 travel book The Canoe and the Saddle, referred to the mountain as Tacoma and for a time, both names were used interchangeably, although Mt. Tacoma was preferred in the nearby city of Tacoma.[20][21]

>In 1890, the United States Board on Geographic Names declared that the mountain would be known as Rainier.[22] Following this in 1897, the Pacific Forest Reserve became the Mount Rainier Forest Reserve, and the national park was established three years later. Despite this, there was still a movement to change the mountain's name to Tacoma and Congress was still considering a resolution to change the name as late as 1924.[23][24] After the 2015 restoration of the original name Denali from Mount McKinley in Alaska, debate over Mount Rainier's name intensified.[25]