What is the official name of the guy in the restaurant who takes the car from the customers and then returns the cars back to them when they finish visiting the restaurant?
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The term is valet.
Wikipedia has a whole page on it. Though I could not find a clear definition in any dictionary, a paragraph from the Wikipedia page says it all.
Valet parking is a parking service offered by some restaurants, stores, and other businesses, particularly in North America. In contrast to "self-parking", where customers find a parking space on their own, customers' vehicles are parked for them by a person called a valet.
Down there on the page:
parking valet – a service employee who parks cars for guests, only from 1960.
Things apart, as J.R. describes (Thanks J.R.), it's better to say - The valet parks the car for the customer. If you still want to use receive, you may say The valet receives an order of parking a car from its owner.
Apart from that, there are professional services as well. They are defined as car valeting services.
A 'Valet' is a person who takes a customer's car (in your case, a restaurant).