Is it mandatory to show user name next to the user icon?

I've come across this simple question while designing an application. The application requires a person to login to the system. When logged in, there will be an icon on the top right of the header which will have a context menu.

Now I've decided it to look in the following way.

^{download bmml source – Wireframes created with Balsamiq Mockups}

Now is it mandatory to show the user name next to the icon? if so, could any one explain me the rational in it.

Thanks