Yes, Mount McKinley was named after President William McKinley. The mountain was originally named Denali, which is a Koyukon Athabascan word meaning "the high one" or "the great one". In 1896, a gold prospector named William Dickey suggested renaming the mountain Mount McKinley in honor of the 25th president of the United States, who was assassinated in 1901. The name Mount McKinley was officially adopted by the United States Board on Geographic Names in 1917.
In 2015, the United States Board on Geographic Names voted to change the name of Mount McKinley back to Denali. The name change was supported by the Obama administration and Alaska's congressional delegation. However, some people, including many Alaskans, opposed the name change. They argued that the name Mount McKinley was part of the state's history and that it should not be changed.
The name change to Denali was made official in 2016.