Whether a domain is taken or not doesn't indicate much. Hopefully, a domain is taken when you set up hosting. It's just that the system has no reliable way of finding out if it was taken by you.
Once you have a hosting plan, you can add as many domains and subdomains as you'd like for no additional charge. But you need to Register a domain before you can host it. These are two separate steps. Start with Registrations if you want your own domain name. Otherwise, you can create an EXAMPLE.dreamhosters.com site on your existing plan without having to pay for a registration. Just pick a subdomain instead of EXAMPLE and you can begin.