Only in the US or everywhere? I see there are anonymizing services to mask the domain details so that any whois query returns a pointer to their office rather than the effective domain owners. A service that does the opposite might be handy for example to expose spammers.
Anywhere. Yes, there are "whois guard" services, but that's actually email relays (like aliases). You must provide your identity information (name, surname, other passport/id data, address, etc.) to buy a domain name.
Any "privacy-oriented" registrar just hides that information from whois records, but you still share it to registrar, so in case of government requests or data leak your PII will be exposed.
There is no anonymity in internet, only pseudoanonymity.
I have yet to be asked for a passport and I own a few region locked domains (ex. .EU). That said there are anonymous domain resellers that basically register the domains on themself. It's more expensive than the usual free whois guard but it's not unheard of.