Dr Shazz is a fictional beverage brand often referenced in the show. Perhaps it's to avoid product placement or copyright/trademark infringement; the name might be a reference to Dr Pepper. It's analogous to Super Fun Guy, a comic book series made up for the show.
Sometimes containers of a Dr Shazz product are used in a mission. For example, in Maroon 8 Happy uses a bottle of Dr Shazz Active as emergency hydraulic fluid. (Toby had brought it for honeymoon hangovers)