The Site title (blog name) and/or the optional Tagline can be changed on the top of this page at any time. > Settings > General ..."save changes".
That is exactly where search engine spiders look for the site title and removing it from there can cause issues with getting your content indexed.
NOTE: Note that the site title (blog name) and blog address URL do not have to be the same. but it's better SEO if they are.
You cannot edit any URL. 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/