Is it mandatory?
Could it help the user?
Many users don't use "real" nicknames when registering, so its not like everyone is using the same nickname on every service and remembers his own nickname.
Also you have people that register multiple accounts, so it would make it easier for them to distinguish between them.
Last but not least, showing the nickname can add personal value if you combine it with greetings etc.
For example instead of just showing the nickname in front of the image you could add a "Good morning Imesh" etc. of course this could be a bit tricky.
But as i said, its definitely not mandatory, you can save a lot of visual real estate by not displaying the nickname, the worst that happens is that the user clicks on the profile image/arrow and finds his nickname there.
Youtube does not show nicknames, Dropbox does not show nicknames etc.