Apple - Hide username from menu bar
- Open System Preferences
- Select User & Groups
- Select Login Options (not Login Items)
- (Click the lock to make changes at the lower left corner of the window)
- Uncheck "Show fast user switching menu as ...
You just have to press the Command key while dragging the username out of the menu bar like you would to remove a dock item.
This is the fast user switching menu, which can be Command + dragged off.
Further settings can be accessed through the users & groups pref pane: