word choice - What is the job title for a "car servant"? - English Language Learners Stack Exchange
word usage - Is someone who drives a car a rider? - English Language & Usage Stack Exchange
A person who drives a car?
Describe the person who drives this car
Most English speakers employ the French loanword “chauffeur” to describe this profession.
A chauffeur is a person employed to drive a passenger motor vehicle, especially a luxury vehicle such as a large sedan or limousine.
Source: Wikipedia entry for “Chauffeur”
You could also just say “driver”.
driver noun \ˈdrī-vər\
: a person who drives a car, truck, etc.
: a person whose job is to drive a vehicle (such as a taxi, truck, or bus)
Source: Merriam-Webster definition of “driver”
If they are people who work in hotels and performing services like this is a part of their job you can call them "hotel valet".
In a car, a rider is usually a passenger, not the driver.
Rider — Vocabulary
n. 1.a. a traveler who actively rides an animal (as a horse or camel)
n. 1.b. a traveler who actively rides a vehicle (as a bicycle or motorcycle)
n. 1.c. a traveler riding in a vehicle (a boat or bus or car or plane or train etc) who is not operating it
I have to say that I have never come across rider when driver or passenger would be the accepted and common usage to cover a car. However, your question is interesting as I consider it perfectly correct to say, "He [neighbour] gave me a ride to work in his new car". To my way of thinking I remain a passenger in my neighbour's car and not a rider in this situation or context. . I wonder if we have a clash of American English versus British English here? In the UK it is common to ask someone if they would like a lift to work and this would be readily understood whether the mode of transport is a car or a motorcycle. However, I don't think lift would be understood in American English in this context whereas ride to work would be. But then the situation becomes even more complicated because we talk about a pillion passenger (BE) in the context of a person who sits behind the rider (the person in control) of a motorcycle.
Pillion passenger: A pillion is a mostly British English term for a...seat behind the main seat...[of a] motorcycle...A passenger (my emphasis) in this seat is said to "ride pillion"... (Wikipedia)