what is the hook name in order to alter theme function of specific element
You can use hook_theme() function to use custom item list.

Hook theme:

function mymodule_theme($existing, $type, $theme, $path)
{
  if ($type == 'module')
  {
    return array(
      'custom_item_list' =&gt; array(
        'variables' =&gt; array('var_name'=&gt;NULL),
        'template' =&gt; 'custom-item-list',
      ),
    );
  }
  return array(); //will raise fatal error if void
}


Call it as usual:

theme('custom_item_list', array('var_name' =&gt; mymodule_variable()));