At racedepartment no, our server is set to say your full name. On other servers it depends on the settings of the particular server. You probably can change a setting somewhere on your own computer to only show your nickname.
But if you also race at Racedepartment you need to check every time if the setting is correct, so showing your full name, otherwise your not allowed to join..
We do that because it increased decent driving if you wondered.
Don;t know myself how to change it or in which file you must look if you do want to change te settings, Tried the multiplayer.ini file? That would be my first guess to look for such a setting.