What is the specific name given to the person who drives the train? Is there any other way of calling the name despite calling them as engineer or engine driver?
The more common use is a Railroad engineer.
Which is an engineer (in America and Canada), engine driver, loco pilot, motorman, train driver (in Britain), is a person who operates a train. The driver is in charge of, and responsible for driving the engine, as well as the mechanical operation of the train, train speed, and all train handling.