How to add a referenced taxonomy term name to the node title in page-title.html.twig
Posting this answer to help those trying to accomplish the same thing. I was told the code above had security vulnerabilities (which has since been removed see comments below).  On the Drupal Slack channel, someone pointed out the following concern with runwithscissors' answer: 


  "This code is potentially dangerous:$variables['title'] = \Drupal\Core\Render\Markup::create($new_title); A user could set &lt;script&gt;alert("foo")&lt;/script&gt; as the Node or Term title and potentially execute code on the site. Typically you don’t want to ever create Markup objects manually. For what you’re doing, I’d suggest setting $term_name to a new key in $variables, then forming your combined title in the Twig template like {{ term_name}} {{ title }}"


So what i ended up doing was adding this template_preprocess_page_title to my MY_SITE.theme file. 

(Note:  field_manufacturer is the specific field for my use case, so you would need to change all instances of that to your taxonomy reference field name.)

/* Add field_manufacturer to all node titles with field_manufacturer and not empty */
function template_preprocess_page_title(&amp;$variables) {
   $node = \Drupal::request()-&gt;attributes-&gt;get('node');
   if ($node &amp;&amp; $node-&gt;hasField('field_manufacturer') &amp;&amp; !$node-&gt;field_manufacturer-&gt;isEmpty()) {
     $term = \Drupal\taxonomy\Entity\Term::load($node-&gt;get('field_manufacturer')-&gt;target_id);
     $term_name = $term-&gt;getName();
     $variables['term_name'] = $term-&gt;getName();
   }
 }


This applies to all nodes with the field_manufacturer, but also checks that the term field is NOT empty with &amp;&amp; !$node-&gt;field_manufacturer-&gt;isEmpty()). This was critical as the reference field was not required, so nodes that had the field but didn't have a value crashed the site with Error: Call to a member function getName() on null in template_preprocess_page_title()

Then I copied and overwrote the page-title.html.twig file from my bootstrap base theme which originally renders the title like this:

{% if title %}
  &lt;h1{{ title_attributes.addClass('page-header') }}&gt;{{ title }}&lt;/h1&gt;
{% endif %}


And changed the H1 title line to this:

{% if title %}
  &lt;h1{{ title_attributes.addClass('page-header') }}&gt;
    {% if term_name %}
      &lt;span class="MY-DESIRED-CLASS-NAME"&gt;{{ term_name }}&lt;/span&gt;
    {% endif %}
  {{ title }}&lt;/h1&gt;
{% endif %}


This adds a MY-DESIRED-CLASS-NAME span class to the term_name. Also by putting it within {% if term_name %}/{% endif %} statement, it prevents that class from being rendered in the html where there is no term_name present.

Hope this helps someone!