advice How to prove domain ownership without WHOIS

Do like the marketplaces. Add a TXT file in the DNS records.

Or configure a subdomain with a specific key or string. You could also add a file to the site that contains a key, or you could add a file to the site containing the key in the filename.

The problem is that the key has to be created by someone that is trusted and is specific/unique to you. That is what some marketplaces do. If you want to list a name on my marketplace, I generate a secure hash unique to you and challenge you to place it in you dns txt/cname record...

You could use your personal name vs a key, or your business name or an established site's domain name; something specific to you that others could not add to your site/dns. Someone could add this to their site/dns to pretend to be you, but that is another issue

If a buyer wants proof that you own a name, you could say: visit billytucker.example.com or aaahosting.example.com. example.com would be the domain name that the buyer might doubt that you actually own.

A third party service that generates a secure key unique to your person/business or established domain/site would be an interesting service Just like a marketplace does, but in this case, only for the purpose of helping a domain owner prove that they indeed own/control the name...

Most markeplaces would automate the checking of the key, so they don't have to waste time in that regard; if it's to convince a buyer, then contacting you via whois might be the easier approach