There's no single answer to who owns the "fastest car in the world" because different cars hold different speed records under different conditions (e.g., closed track vs. public road, production car vs. prototype). Furthermore, the records change periodically as new cars are developed and tested.
The people who *own* the fastest cars are typically wealthy individuals, car collectors, or companies themselves (manufacturers testing their own creations). The information on specific ownership is usually not publicly available.