You are probably overthinking a bit, but you should be able to rely on the hosting company not to give out your details. If that's not the case, change the hosting company. Hide your domain's whois, and that's about it.
Another quite obvious thing is not to have your details on your website.
Diplomat is right that you can get Whois protection and a hosting company that doesn't give out your details. You can also hide your hosting provider's IP address with Cloudflare.
In the EU for example it is illegal to stay anonymous when collecting data (GDPR), even if you use Google analytics for example.
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