Domain anonymous
Some people prefer to register a domain anonymous because of different reasons. If you register a domain anonymous nobody can see, who is the owner of the domain. This is called privacy protection and a lot of hosting providers offer this service. A privacy protected domain is also meaningful to protect against spam. Privacy protection is not available for every domain ending. It's not possible for country-specific domains. If you want to register a country-specific domain a domicile in the sepcific country is needed. The only way to register a country-specific domain is to use a trust service. The provider will be entered as owner of a domain. But you have a contract with the provider, that you are the owner of the domain.
Offshore domains anonymous
If you register a non-country-specific domain (e.g. .com) privacy protection is available for almost all endings. A specific domicile is not needed and a trust service is not needed,too. The hoster will be entered in the Whois database of the domain an nobody is able to see the owner. Some hoster offer privacy protection for a few dollar or for free.
But remeber if you register a domain anonymous always the laws of the country where you have your domicile are valid. For a example you havea country-specific domain there is often the duty of an imprint. If you don't want to risk a written warning you can register a company in the specific country. In the internet you can find a f ew websites where you can register a offshore company. Popular offshore countries are the Netherlands or Panama. Even an anonymous company foundation is possible.
And if you want to stay completely anonymous , also against the hoster, this is possible. A lot of offshore hoster offer complete anonymity. This is possible if you pay with Bitcoin or an other crypto currency. Basically it's no problem to host complete anonymous.
If you decide to create a website, one of the first decisions is the domain name and the domain ending. The name of the domain should describe your company or the activity. This is an important point for SEO (search engine optimizing). The name should include the most important keyword, which you should be found. And don't forget the edning, the ending is important,too. You can choose a country-specific ending (.nl, .ch, .de) or a not-country-specific ending like .com. The language of your website and the specific ending should be the same.