Hello Edhor,
Thank you for your reply, the easier way to achieve it is by installing any login module available for Joomla, when the user is logged in it will show the name of user and logout option if no user is logged in it will show login button.
If you do not want to show login or logout buttons or form and would like to show just the name, then little customization will be required. its a job of 1-2 Hours.
-Abhishek
Team sellacious