Do not display user name in the panel
Solution 1:
(If you dont want to install other programs)
Open a terminal and use this command to disable the name display
gsettings set com.canonical.indicator.session show-real-name-on-panel false
To revert it back simple use
gsettings set com.canonical.indicator.session show-real-name-on-panel true
After using one of the commands you need to log off and back on or use unity --replace &
to reload unity.
You can also remove the user switching menu from the indicator panel with
gsettings set com.canonical.indicator.session user-show-menu false
and enable it with
gsettings set com.canonical.indicator.session user-show-menu true
but if you do so you will disable both the username and the user switching indicator. You cannot remove the user switching menu while keeping the username indicator.
Solution 2:
open dconf-editor, go to "apps -> indicator-session" and unmark "user-show-menu"
logout and login again