It's entirely up to you. If you want a URL like www.lairofthedevil.dreamhost.com then this is called a 'sub-domain'. A sub of the domain dreamhost.com. I believe these are free for all customers who have an account with Dreamhost.
Alternatively, you can register your own domain, so you can have a primary domain of your own, like www.lairofthedevil.com. This would cost you registration fees, which I think stands at around $25pa.