To change your screen name, go to Account Settings -> Personal and change your Screen Name there. This name will be displayed when posting messages and comments in the groups.
To make sure this name is visible in your personal profile (instead of your first- and last name), you will need to adjust your Privacy settings. Go to Privacy in your Account Settings and choose "Screen name" at "Visible name"
Tags: screen name, name, privacy, not visible, adjust, account settings, personal