Note that this means you are technically not the owner of the domain, and you may be limited in your ability to transfer it, sell it, or do other things with it. Permissions are limited to what the registrar allows instead of what ICANN allows, although in most cases they give you nearly full control. You'll just have to read their terms if you want to know what you can do with it.
This is a myth. ICANN has published requirements on how private registrations must operate; ownership of the domain always goes to the paying owner, not the registrar.
Depending on the registry, it's unavailable or at least against the rules for some tlds.
And yet other TLD registries are sensible enough to make privacy the default for private individuals. .EU isn't bad in this regard, and others like .SE even go so far as to hide your name (most only hide your postal, email, telephone)
Frankly I don't know why anyone who can avoid it would want to touch Verisign TLDs with a barge pole... they have the continued gall to keep putting their prices up despite more competition than ever, and fail to raise the bar on basics like whois protection. Even .UK domains can be had for $5/year with registry level whois protection for heavens sake.
For example https://who.is/whois/habinow.com is one of mine that is private
while https://who.is/whois/ycombinator.com is pubic and shows Nicholas Sivo as the admin and an address and phone number for y combinator
When you register a domain, it's a requirements that you list contact information publicly. Companies usually don't mind doing this but many people don't want to list their home address and phone number for the world to see. Private registration lists a proxy company's information as the contact for the domain and they forward the information to you.
