How to change the email notification recipient (user) for new comments?

There’s a great article explaining how to hook into 2 filters for this at https://web.archive.org/web/20200216075253/http://www.sourcexpress.com/customize-wordpress-comment-notification-emails/

To send your notifications to a particular user and not the site admin, try this for a user with ID 123:

function se_comment_moderation_recipients( $emails, $comment_id ) {
    $comment = get_comment( $comment_id );
    $post = get_post( $comment->comment_post_ID );
    $user = get_user_by( 'id', '123' );

    // Return only the post author if the author can modify.
    if ( user_can( $user->ID, 'edit_published_posts' ) && ! empty( $user->user_email ) ) {
        $emails = array( $user->user_email );
    }

    return $emails;
}
add_filter( 'comment_moderation_recipients', 'se_comment_moderation_recipients', 11, 2 );
add_filter( 'comment_notification_recipients', 'se_comment_moderation_recipients', 11, 2 );