How to add a variable to a twig field template? On a node page I would like to add the node title to the output alongside another another field (the example field). 

I have created a new field--field-example.html.twig but am unable to access the node title variable as it is not available in the field template.

I need to add the variables into the theme preprocess: themename.theme.

How do I add the variable in themename.theme and what would be the corresponding entry in the field--field-example.html.twig ?
Since you asked about passing the node title as a variable via the .theme file, you could use template_preprocess_field to do something like this:

  function themename_preprocess_field(&amp;$variables, $hook) {
    if ($variables['element']['#field_name'] == 'field_example') {
      $variables['node_title'] = $variables['element']['#object']-&gt;getTitle();
    }
  }


then in your field--field-example.html.twig you could simply just use {{node_title}} to render the node title.

Also see 4k4's answer below.