You cannot edit a URL so be clear about that please. If you want to change the blog address ie. the URL starting with http:// then you must be logged in as Admin under the exact same username account that registered the blog to do that and the URL you desire must be available. If so then you can change the URL by using this guide http://en.support.wordpress.com/changing-blog-address/
curlyheadedblackgirl.wordpress.com is no longer available. The authors have deleted this site.
Deleted blog URLs are not recycled, regardless of who registered and deleted them and no exceptions are made.
However, the good news is that you can register another .wordpress.com blog http://en.support.wordpress.com/register-a-blog/
Then you can register a domain via a domain mapping upgrade because it does not matter what the underlying .wordpress.com address is when you are domain mapping.