The story
Named after American businessman and attorney Charles E. Rushmore (1857–1931). In 1877, the United States broke the Treaty of Fort Laramie and asserted control over the Black Hills area, leading to an influx of settlers and prospectors, among whom was New York mining promoter James Wilson, who organized the Harney Peak Tin Company, and hired Rushmore to visit the Black Hills and confirm the company’s land claims. Rushmore visited the area on three or four trips over the span of 1884 and 1885. During one of these visits, Rushmore was traveling near the base of the peak and, impressed with it, asked his guide, Bill Challis, the mountain’s name, who replied that the mountain did not have a name, but that it would henceforth be named after Rushmore. The name “Mount Rushmore” continued to be used locally, and was officially recognized by the United States Board on Geographic Names in June 1930.
Etymology from Wiktionary, CC BY-SA 4.0.