Your username serves two purposes. First, it’s your login for the back-end administration of your website. Second, it’s the public name that will appear on your blog, whenever you comment on other WordPress sites and when you join other blogs. The two don’t have to be the same.
There are two ways to change your Username.
1) If you want to keep the same login and simply want to change the way your username appears on the internet: Go to Dashboard> Profile > My Public Profile. Scroll to “Display name publicly as” and enter your name the way you want. Then click the Update button up top.
2) If you want to change your username completely, both in the back and front ends (note this affects other things like your Gravatar): Go to Dashboard> Profile > Personal Settings > Scroll to Account Details. Then Change “Username
Read more on my Blundr.