When we register a username account here the email address we provide becomes our unique identifier. When we are logged into WordPress.com and register a blog it's registered to that username account we are logged in under and to the email address which is our unique identifier. We can register as many blogs as we wish and provided we are using the same username account then all the blogs will be registered under it and the associated email account. We can change our "display name" but that display name will appear on all blogs registered under the same username account.
http://en.support.wordpress.com/email-address/
http://en.support.wordpress.com/change-your-username/#change-display-name-nickname

In order to completely separate the blogs that you do not want to be associated with each other you register another username account using a different email address when you are logged out of WordPress.com. http://en.support.wordpress.com/register-a-blog/ Then you add the new username account as an official user of the blog, and designate them (ie. you) as an Admin. Next you transfer one of the blogs to the new username account using this process. http://en.support.wordpress.com/moving-a-blog/#transferring-your-blog-to-another-user-or-account