I want to make sure I understand exactly what you want to do. Do you have subdomains like thing1.example.org and thing2.example.org and you want these to be fully fledged domains like www.thing1.org and www.thing2.org?
If so, you need to register the domain names thing1.org and thing2.org. You will then need to migrate the content on your servers from thing1.example.com to thing1.com - or you can redirect or shadow them, but the best thing is to probably move them. You'll probably need to ask around for advice on this migration if your site uses WordPress or some other web application. If your site is just static content, then it's usually a little bit easier.
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