How can I add a real name field beside username to user information?
Simply add a textfield (or two, if you want first/lastname) to your users at admin/config/people/accounts/fields. That will allow them to enter their realname and it will be displayed on the user profile page.

And if you want to display that name in various places (like node author), that's exactly what Realname module is for. It allows to configure the displayed name based on tokens (which can either be profile fields or user fields).