1) Click on your name in the upper right corner and select "Users and Groups Preferences..." from the menu that drops down
2) On the screen that opens, click on Login Options at the bottom of the list on the left hand side (with a house next to it)
3) If the writing that appears on the right hand side is grayed out, click on the padlock at the bottom that says "click the lock to make changes" and enter an administrator's user name and password (if you're the only user, or are an admin user then just enter your password). If they're not, then skip to step 4
4) Click the checkbox next to "show fast user switching menu as" on the right hand side
You should now no longer see your name showing