Change the word "Register" in the wp adminbar

Trying to create a function that will parse the Register link in the admin bar to change the text. I’ve got it deployed on multisite and I want to clarify how it reads.

I want it to say something like “Register a new [insert network name] account”

This is what I have so far but it isn’t working (there is probably something more complex needed), cqn anyone help me tune this up?

// Change the default register link to something branded
function branded_register_link() {
echo '<a href="' . site_url('wp-login.php?action=register', 'login') . '">' . __('Register a new network account') . '</a>';
}
add_action( 'wp_register', 'branded_register_link',);

The original code snippet (as far as I can tell) comes from wp-includes/general-template.php and it is this:

function wp_register( $before = '<li>', $after = '</li>', $echo = true ) {

if ( ! is_user_logged_in() ) {
if ( get_option('users_can_register') )
$link = $before . '<a href="' . site_url('wp-login.php?action=register', 'login') . '">' . __('Register') . '</a>' . $after;
else
$link = '';
} else {
$link = $before . '<a href="' . admin_url() . '">' . __('Site Admin') . '</a>' . $after;
}

if ( $echo )
echo apply_filters('register', $link);
else
return apply_filters('register', $link);
}