The plugin uses display_name by default. All users can choose themselves how to display their name on the website from their profile:
Not sure how WordPress determines the default value for display name in your install, though.
If you want to overwrite the behavior via the extension plugin, then I assume changing the return statement (line 22) to the following should do. At least, if your users filled in these values during registration and the values are stored in the WP_User object.
