advice Can we look up domains based on DNS?

With the zone files yes. They are available for .com/.net and many gTLDs. ccTLDs: sometimes...

Yup, you can use the dns.link service. Enter the nameserver you want to lookup and it gives a daily change list of the domains for that nameserver.

If they are on shared hosting, then there may be multiple owners. Also, you may find that some domainers use multople dns servers, so you may not get all of their names.

Don't forget that many use dns forwarding as well.

Related:

• Checking domain name availability without using a website
• http://viewdns.info/
  
• https://mxtoolbox.com/

Hope that helps,