Anonymous hosting means the provider does not collect identifying information beyond what is technically necessary to deliver the service. At minimum: no government ID, no phone number, no full name required for signup. For payment: the provider accepts cryptocurrency (ideally Monero for unlinkable payments). For jurisdiction: the hosting country does not legally require providers to collect and retain customer identity documents for hosting services.
Many providers claim anonymous hosting but require an email linked to a real identity, or accept only credit cards that create a financial paper trail. True no-KYC hosting means: email-only signup (ideally from a throwaway or ProtonMail/Tutanota account) and Monero or BTC payment. The jurisdiction must not impose mandatory identity verification on hosting providers - Romania and Iceland both meet this criteria. US-registered providers cannot credibly offer anonymous hosting regardless of marketing claims.
Note: even with anonymous hosting, your traffic, IP address, and online behaviour remain linkable unless you also use Tor or a VPN to access the control panel and connect to your server.