femdomtimes, I’m sorry, but we do not reuse or reassign deleted blog names on WordPress.com. You will need to select a different blog name. For full details, please see:
There is one other option available to you, though. You can purchase a domain name and map that back to your WordPress.com blog. In that case, nobody would ever see the underlying WordPress.com URL. They would just see your purchased domain. For full details, please see:
eclecticdreamer, I'm sorry, but deleted blogs cannot be restored or reused. Deleting a blog is permanent and the name cannot be used again. There are several warnings about this on the Tools -> Delete Site page and in the help pages, and you are required to confirm the deletion by email.
You can start a new blog by logging in to WordPress.com and then going to http://en.wordpress.com/signup/
With any blog, you can also use your custom domain with Domain Mapping upgrade. http://en.support.wordpress.com/domain-mapping/