@OP: You should go to this link:

http://support.chess.com/Tickets/Submit

and click the radio button for Account Issues & Username Changes.

You can also do this yourself by clicking on your username at the top right of the page next to the logout X.  One issue, however, is usernames cannot have any spaces or symbols other than - or _ 

You could always have a username and then fill in your real name so it appears underneath. You would also do this from the edit profile page. http://www.chess.com/members/view/ACEChess - for an example. :)

Where exactly in my profile I may add my name under my username?
I just checked there is no box for that, do you use the "Occupation" box?

I see it here, at the top: http://grab.by/iD20

Hoi Mark heel gemakkelijk dus zie de opmerking van Calamondin. Heb het zelf geprobeerd. Ging in 1keer goed. Gr. Robert

Je kan 1 keer zelf je naam veranderen als ik het goed voorheb.

And you can change it only once..As i found out the hard way.

N' had to beg staff for my identity back.

That was what I said Stevie but in Dutch 

Clever clogs

I must say,that suits you better. A man of your chess calibre that is.