Anonymously.io is an anonymous hosting provider that only accepts Bitcoin payments. Only an email is required to register with them. You don't fill any personal data, and you will never have to.
They have their own private servers in various datacenter locations in the Netherlands.
Anonymously has build their own Bitcoin payment gateway, so no third-party is involved.
Anonymously has a specific set of rules that everyone has to abide by. Nothing illegal is allowed.