I am interested whether it is legally possible for a private person to register a domain name which includes city or country name extended by other phrases? Such as carservicecityname.com or countrynamecarservice.com?
Welcome to WSE. For .com/.net/.org there is no limitation on domain ownership except in the case of breach of trademark or copyright (ie. cocacola). And even with that, it would need to be a trademark on a word, words or phrase, not a logo, for you to be unable to register it without losing it.
City and country names and landmarks are not covered by trademark or copyright.
There are other regulatory limitations on other localised (such as .au ) or specialised domain names (such as .pro and .travel) however I know of no other domain names where the above isn't true for city and country names and geographical landmarks.
According to copyright laws, you can't use a name for a business copyrighted for your business exactly like that. Example: BMW
But with within the cyber space, you don't need to worry much.
You have the right to choose the domain names. Even you can get a domain name bmwfanstokyo.com
But for good or bad, these companies might have purchased most of the good sounding and spelling domains that they would need in their near or far projects.
There might occur a problem only when you have content that they have issues with.
For example, Sony has the copyright to broadcast the IPL live and you are giving an online streaming in your website, they will surely send you a notice after which they will take it forward with the court if you are good enough to drag more or a good amount of traffic like them.