How do you manage to win a medal at six straight Olympics and remain more or less unknown? The answer: win by shooting a gun. American skeet-shooter Kim Rhode last week became the first athlete, male or female, to win a medal at six summer games and the first on five continents, but don’t look for her on a box of Wheaties.

Mrs. Rhode, who won a bronze medal in Rio, has received little media attention despite her historic feat. The 37-year-old also lacks a single major corporate sponsor, though her ammunition and training...