This is something your domain provider has to offer to you. It is usually a paid service. Not all TLDs allow it though - so depending on your domain ending you might be out of luck. I don't know your intentions, but if you want to evade prosecution because of the traffic going through your TOR node this will not work. Even with whois privacy enabled your provider must disclose your identity to prosecution. Even if they weren't the A record (IP address) of your domain would link the domain to your server and would open another way to identify you through your hosting provider or ISP.

The information returned by whois depends on the registry. For example, most registries for European TLDs basically just show whether the domain is registered (I say “most” because I'm not sure whether it's actually all or if there are exceptions, but I know .de is like this). In that case, there aren't even “whois privacy” services available from registrars. For TLDs from other countries or gTLDs, this might vary.

In either case, do note what the other comment says. Whois is not the only way to identify who runs a service.

it returns a lot of information such as registrar name, abuse contact, creation date... even though i paid extra for "whois privacy."

If you didn't pay for whois privacy, it would most likely return your actual name, email address, phone number, and home address instead. “Whois privacy” just means your registrar inserts their information into these fields instead, and forwards any mail they might get to you.

I have my domains through cloudflare, and they are basically empty:

Domain name:
        xxxx.uk

    Data validation:
        Nominet was not able to match the registrant's name and/or address against a 3rd party 
source on 06-Jun-2023

    Registrar:
        Cloudflare, Inc. [Tag = CLOUDFLARE]
        URL: https://cloudflare.com/

    Relevant dates:
        Registered on: 06-Jun-2023
        Expiry date:  06-Jun-2026
        Last updated:  07-May-2025

    Registration status:
        Registered until expiry date.

    Name servers:
        paul.ns.cloudflare.com
        tia.ns.cloudflare.com

Disclaimer
Domain name:
        xxxx.uk

    Data validation:
        Nominet was not able to match the registrant's name and/or address against a 3rd party 
source on 06-Jun-2023

    Registrar:
        Cloudflare, Inc. [Tag = CLOUDFLARE]
        URL: https://cloudflare.com/

    Relevant dates:
        Registered on: 06-Jun-2023
        Expiry date:  06-Jun-2026
        Last updated:  07-May-2025

    Registration status:
        Registered until expiry date.

    Name servers:
        paul.ns.cloudflare.com
        tia.ns.cloudflare.com