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Transform http://checkman.wordpress.com into www.checkmanblog.com ??
WordPress.com and wordpress.org do not operate on the same code base for a comparison read this
To do what you want you will have a choice of purchasing a domain and then downloading a free wordpress theme from wordpress.org to your own server or hiring a webhost to do it for you. More information is over here http://wordpress.org/hosting.
Checkman, I think you want to just change your domain name. Currently, that feature is not being offered by WordPress.com blogs, though it is under future consideration as a paid service. Follow the instructions timethief has given you for finding a paid hosting service and starting your own blog there. You can still use the free version of WordPress and export your WordPress.com posts using the EXPORT to XML feature and then import them into your new site.
You should also know that there currently is no rerouting or redirection from your wordpress.com blog to your new one, so you will need to leave a post with instructions to your new blog.
Domain mapping is currently in testing.
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