WASHINGTON—The Marines won’t say it out loud, but everyone knows that Cpl. Chesty got promoted to sergeant this summer not for being a good Marine, but for his in-your-muzzle confrontation with the top dog in the Pentagon.

Just two weeks before his promotion, the Marine Corps mascot, an English bulldog formally known as Chesty XIII, had a run-in with Bravo, Defense Secretary Leon Panetta’s golden retriever. Chesty, usually known for happily mugging for photos with kids, revealed his inner grunt when he spotted the larger dog...