Hi Joao,
I'm assuming you are using the Gravity default dnn skin.
1 - Get the skin files from /Portals/_default/Skins/Gravity - Those are the files with extension .ASCX
2 - Open them and locate dnn:USER
3 - Inside that tag add another parameter like this ShowUnreadMessages="false"
That's it. You also have the option ShowAvatar="false", which will hide the user thumbnail.
Cheers,
Aderson