If you're looking for anonymous domains and want to pay with Bitcoin, you might want to consider using RoboSats to buy Bitcoin anonymously first. Then, you can use those sats to purchase your domain.

WhiteEyeSats helps you to coordinate your RoboSats trades!

Check them out:

Clearnet: https://clearnet.whiteyesats.website/

Tor: http://s4usqbcf2pk2xwghdzaggrxd3paiqpvnl4lm2dxp6dec3wbclgbdyiyd.onion/