To register a domain anonymous may have different reasons. For example you don't want, that others can see the whois-entry of your domain and find out who the owner is. Thereby you can protect against spammer. But remeber there are differneces, which ending you want. If you take a country-specific domain you need a domicile in this country. If you don't have a domicile in this country, there are hoster, who offer a trust service. If you need a trust service, the hoster/provider will be entered in the whois-entry as owner. However you have a contract with the hoster, that you have all rights about the domain.
It's easier if you register a non-country-specific domain (e.g. .com). For this domains you don't need a special domicile. The webhoster is here entered as owner, too. But you don't need a trust service, what usually is liable to pay costs. This is called privacy-protection. This service is offered by a lot of webhosters for free or a little fee.
Keep always in mind, if you operate an anonymous domain, always the laws apply, where you have your domicile. If you have a .de domain for example, you have a imprint duty. If you really want to keep absolutely anonymous, without risking a written warning, you can establish a company in the particular country. There are a few websites in the internet, who offer the foundation of a offshore company. Offshore countries are very popular ( Panama, Netherlands, UK). If you want to stay anonymous against your webhoster, too, than you should join a provider accepting Bitcoin. A lot of webhoster offer basically to stay anonymous.
Here are some domain endings, where you don't need a trust service. Anonymization is offhand possible (privacy-protection):
.com, .net, .org, .info, .biz, .name, .mobi