Force display name as full name

This is set during user registration. You can change the value per filter 'user_register'.

Sample code, not tested:

/* Plugin Name: First name plus last name as default display name. */
add_action( 'user_register', 'wpse_67444_first_last_display_name' );

function wpse_67444_first_last_display_name( $user_id )
{
    $data = get_userdata( $user_id );
    // check if these data are available in your real code!
    wp_update_user( 
        array (
            'ID' => $user_id, 
            'display_name' => "$data->first_name $data->last_name"
        ) 
    );
}