If the driver is working as an independent contractor, as opposed to working for a company directly, it may make sense to sue the driver in the instance of an accident. Trucking companies are liable for the actions of their employees, but independent contractors are not necessarily employees. If the truck driver used their own truck, assumed their own expenses, and was paid per job, you may have a stronger case in court to sue the driver.
Even if a commercial driver is a paid employee, there are certain instances in which they can be held liable for their actions. If the driver was using the vehicle for extra-business purposes at the time of the accident, you have a stronger case to hold the driver personally liable. You might also have a stronger case against the driver if their negligent or illegal actions contributed to the cause of the accident.