You can. Just click the three bars next to your name at the top of the page and choose Settings/Account. You'll find your user name under the General Account Settings Tab.
If you change your user name, this will change both the user name you use when logging in to Clipparoo, and the end of your personal Clipparoo url. When you access your Clipparroo account, it is located at www.clipparoo.com/yourusername, and the url generated for all of your Clippboards will also include that user name (www.clipparoo.com/yourusername/clippboardname). So if you have bookmarked that direct link, or shared it with anyone, the link will change as your user name changes. Your Original url will no longer work if you change your Username.