Is it possible that my domain is registered not to me, but to some other legal entity or individual not related to me?

Question

Domain name market

I just look at whois, the mail of the name registrar and private person are indicated there

Answer 1

This is the basic hiding of personal data.
You can write a test letter to the specified postal address - if it comes to you, then there is no reason to panic.

Answer 2

If you go to the registrar in your personal account and see your domains there, there is no reason for concern. You know what is written on the fence. This thing is called "contact protection". The registrar enters a fake mail there, when clicked on, a form will open for typing a letter that will come to the soap that you indicated to the registrar.
If you clicked, typed, sent - and it came to you - then everything is definitely fine :)
And of course it can be so :)