问题的第二部分通过将此代码放入主题函数中来解决。php文件：

// First name as default display name

add_action( \'profile_update\', \'set_display_name\', 10 );

function set_display_name( $user_id ) {

    $data = get_userdata( $user_id );

    if($data->first_name) {

        remove_action( \'profile_update\', \'set_display_name\', 10 ); // profile_update is called by wp_update_user, so we need to remove it before call, to avoid infinite recursion
        wp_update_user( 
            array (
                \'ID\' => $user_id, 
                \'display_name\' => "$data->first_name"
            ) 
        );
        add_action( \'profile_update\', \'set_display_name\', 10 );
    }
}