How to render the same field twice but with different name/id attribute?
The select element don't have #name atribute (Form API Reference). You can implement the hook_form_alter() in a custom module.

/**
  * Implements hook_form_alter().
 */
function YOUR_MODULE_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  if($form_id == 'YOUR_FORM_ID') {
    //here you can make the copy
    $form['field_add_option_copy'] = $form['field_add_option'];
  }   
}


You can read this: Creating modules - a tutorial: Drupal 7.x