Final answer:
Charles Sheldon's strongest claim for renaming Mount McKinley to Denali is the historical use of the name by the indigenous people and its recognition by the Alaskan state government.
Step-by-step explanation:
Charles Sheldon's strongest claim for renaming Mount McKinley to Denali is that it is the name historically used by the native Athabaskan people in the region.
He argues that using the name Denali respects the cultural heritage and traditional knowledge of the indigenous people.
Additionally, Sheldon points out that the name Denali has been widely recognized and used in the region for many years, including by the Alaskan state government.