No, if you bought your own domain address you cannot change it on an existing website. However, you can buy a totally new domain address if you want to, back up your present website to your computer, then upload the info again into your new domain name.
Here is a tutorial on backing up your website: Backing Up Your Website
You just can't type in a new domain name for an existing free website, no. But you can get another free website here at SiteRubix with a new name, and move your info to the new free website.