That sounds like you want Njalla (onion—when v3!?).  It is about twice to tenfold the price; but they are Tor/VPN friendly (no evil-IP account lockout horror stories), and they do not ask any IRL identifying information whatsoever.  No need to make up fake info—no risk of having domains cancelled for fake info.  If you really want, you can even avoid giving a throwaway e-mail address by instead using a throwaway Jabber/OTR address.  They don’t want to know who you are.

The way that works is that legally, they own “your” domain, such that real identifying info of a corporate entity in an exotic jurisdiction satisfies the ICANN doxing requirements that apply regardless of WHOIS-hiding.  The way I see it, that is strictly better than using fake info!  Anonymous parties with fake registrant data have no effective recourse against a bad registrar, anyway; if you are not clearly identifiable and prepared potentially to sue in court, nominal legalities present a distinction without a difference.  You must repose trust in the registrar.  I would prefer to trust a registrar who respects my privacy.

But if you really want, you can enter your real name, snailmail address, and telephone number for the registrant.  This will result in your name being exposed in the public WHOIS, which some people actually want (especially “domainers”).  The form for that is buried somewhere on the domain management page, after you have already registered the domain anonymously.  It is strictly opt-in.

Obviously, they do Bitcoin, including Lightning—also Monero and fully-shielded Zcash, and some oddball WTF shitcoins such as Paypal.  They never used Shitpay.

I have no affiliation with Njalla, other than as a customer.  I am always looking for more options for this class of service; but everything else in my current awareness for fully anonymous domain registration is either even more expensive than Njalla, or of unknown reputation.  For my part, I welcome suggestions.

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Is “KYC” so normalized nowadays, in the sense of “the new normal”, that this is now a normal question?

“Know Your Customer” is a banking-specific propaganda euphemism based in idiocy about so-called “money laundering”.