Not an easy one to answer. I know the story of Sam Wilson who supplied food to the American forces during the War of 1812, but I think Uncle Sam may be just a mythical US national icon much like John Bull in Britain.
Peter, your information is good, thanks... My source says the answer is true and further states this:
--The real Samuel Wilson was born in Massachusetts in 1766, and he banged a drum during the Revolutionary War. By the War of 1812, Wilson had a meatpacking plant that supplied rations to U.S. soldiers. He stamped his crates with a large U.S. on the side, for "United States." A worker joked that since the crates came from Sam Wilson, U.S. really stood for "Uncle Sam." The joke caught on, and soon everyone referred to "Uncle Sam's" crates. Cartoonists drew Sam as clean-shaven until the 20th century, when he was portrayed as tall and bearded.--