Buy with crypto from a registrar that offers Whois Guard e.g. NameSilo or Namecheap or just enter pseudonym and virtual address. Domain registrars dont ask for government ID.
I got the hosting and the domain with my persona paypal.
Its news website, not any illigal thing. Just the freedom of speech is very limited in my country.
This is what crypto (especially monero) and tor are for. You can transfer the domain e.g. to Namecheap and buy Whois Guard but with court order the registrar will probably disclose your infos. If there is a real risk, consider the hosting and domain to be burned and buy different hosting and domain from a different company with bitcoin or monero (either use pseudonym + virtual address or use host like OrangeWebsite which only requires email address).