Hi yourdaynow,

To have your own domain name, you have to pay to get one. You can get one at $10/yr at www.reghub.com

As for hosting your blog on your www.yourblog.com , you can get a web hosting account and setup a "redirect" for your domain name to your blog ( i assume at blogspot)

Alternatively, you can ask your webhost to help migrate your blog data to a new blog software and host everything off on your new web host.

Sound complicated? You may ask if you have any question. I will try to help you.

For hosting needs, i recommend www.mxhub.com