One common name was Smithfield brand BBQ items, which have been around for over 50 years. Today you can go online here and get their famous James River brand BBQ sauce and other products. Below is one of several versions of their drive-in commercials produced in the late 50s, touting their product.
Another BBQ product was Castleberry's Pit Cooked BBQ. For the history of Castleberry's I'll let this informational blurb from their website tell the story:
Castleberry Food Company was founded in Augusta, Georgia on the popularity of barbecued pork and beef recipes of Clement Lamar Castleberry, a gentleman who loved entertaining and expressed it best by serving his guests the best barbecue they ever tasted. By 1922, Mr. Clem was preparing barbecue for crowds as large as 12,000. In 1926, Clem's son, Clement Stewart Castleberry, hit on the idea of canning his father's famous barbecue hash and Brunswick stew. Thus, Castleberry Product Company was established in a humble shed on Fifteenth Street.
During World War II, the firm produced no commercial products, but worked tirelessly producing military rations. Mr. Clem was dubbed "The Rebel with The Pepper Shaker" and the U.S. Army bestowed on Castleberry two "A" awards.
Still located on Fifteenth Street in Augusta Georgia, there are two manufacturing sites which consist of a large 230,000 sq foot facility on 22 acres that processes canned and frozen products and a 25,000 square foot facility that processes fresh vegetables.
Who produced these and other commercials for drive-in snackbars? Go here and here and learn more!