You can host as many domain names as you want all hosted under your account here.
It sounds to me like you didn't register a new domain when you signed up for your account, but just signed up and started hosting a dreamhosters.com subdomain. This is fine. You just need to register and then host a new domain. This domain will count as your free one.
You should start with registering your new domain. The Dreamhost wiki has a lot of information for beginners and experienced folks alike. Here's an article that should walk you through registering your domain:
Your next step will be hosting your domain. What were you looking to do on your domain?
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