Remove the register link from the WordPress wp-login.php script. See blog post: http://snippets.webaware.com.au/snippets/remove-register-link-wordpress-wp-login-php/

register-link-remover.php

<?php
/*
Plugin Name: Register Link Remover
Plugin URI: https://gist.github.com/webaware/11387141
Description: remove the register link from the wp-login.php script
Version: 1
Author: WebAware
Author URI: http://www.webaware.com.au/
*/

/*
copyright (c) 2014 WebAware Pty Ltd (email : rmckay@webaware.com.au)

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License, version 2, as
published by the Free Software Foundation.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
*/

/**
* remove the register link from the wp-login.php script
*/
add_filter('option_users_can_register', function($value) {
    $script = basename(parse_url($_SERVER['SCRIPT_NAME'], PHP_URL_PATH));

    if ($script == 'wp-login.php') {
        $value = false;
    }

    return $value;
});

Did not work for me. Thanks for code. Any idea what filter to add to my child theme functions file if we rename the login page? For security we rename the login from usual one to some text (using WP Simple Firewall plugin).
thank you

Thank you, works great!