When you start a WordPress blog you get a domain name that looks something like this fun.wordpress.com. If you want funhouse.com you must by a domain name and port it to your WordPress.com site. Fortunately you can do this without ever leaving WordPress.com. Go to that sites dashboard and click “Upgrades” and then click “Domains”. Under “Add a Domain” enter the domain you would like to get and click “Add domain to blog”. Fill out the form and make sure to check “Make my personal information private for this registration.” This will cost you an extra $8 but it’s worth it. Total will be $23.
There are other domain options such as domain mapping your domain that you already have for $12 and domain forwarding which you must setup with your domain register.