Wrap the link title in a span, that will get display none. I could have also just removed the title, but I wanted it there for SEO (I guess)

template.php

<?php 

function ross_menu_link__menu_block__menu_social(array $variables) {
  $element = $variables['element'];
  $sub_menu = '';

  if ($element['#below']) {
    $sub_menu = drupal_render($element['#below']);
  }
  $element['#localized_options']['html'] = TRUE;
  $element['#title'] = '<span>' . $element['#title'] . '</span>';
  $output = l($element['#title'], $element['#href'], $element['#localized_options']);
  
  return '<li ' . drupal_attributes($element['#attributes']) . '>' . $output . $sub_menu . "</li>\n";

}