You can check who owns your domain name simply by looking up your domain’s WHOIS record. The person or company indicated as the registrant in the WHOIS record is the owner of the domain. If the registrant data doesn’t show your name and your contact details, you don’t own your domain.
Most registrars sell domain privacy services. The selling point is that WHOIS records are harvested by spammers, and surely you’d like to pay a small fee to receive less spam. But what you’re really paying for is for your registrar to own your domain name on your behalf. If there’s ever a problem with your registrar, they will be the owner of your domain, not you. Good luck suing them for breaking their domain privacy service contract. Quite a few registrars have gone bankrupt or had their registrar accreditations terminated in recent years. In such a situation, ICANN needs your contact info in the WHOIS records when they do a bulk transfer to another registrar. My domain names are very valuable to me. I’d rather get some more spam than to take risks with my ownership of my domains. The article WHOIS Masking Considered Harmful on CircleID discusses this issue in depth.
Another issue are technical glitches. Recently, I looked up the WHOIS records of some domains I had recently transferred to a different registrar. To my surprise, the new registar was listed as the registrant of the domains I had transferred. When I logged onto the registrar’s control panel, the contact details for those domains were totally blank. It seems the contact information was lost during the transfer for reasons unknown, and the registrar had put their own information in the WHOIS for my domain because they have to put in something. Fortunately, all it took for me to fix this problem was to enter my contact information for those domains.