On the action set of the down arrow, configure "on click" event and action as the "Menu", In the parameters, Context as navigation rule which has a logoff option, Format as "Header Menu". By following the above steps, you will be able to show the menu similar to the attached screen.
Oh ok, yes this is very easy to setup in Pega. Adding button with a click event to launch a nav menu will get you the functionality you are seeking. However, if you are seeking that exact styling, then that will likely require some custom CSS or custom images to make the look and feel consistent with your example.