How to get the referenced entity name instead of target_id in Normalizers?
you have the target id so just load the term and send the label instead of target id, something like :

$tid = $node_detail['field_story_type'][0]['target_id'];
$term  =  \Drupal\taxonomy\Entity\Term::load($tid);
$news_data['type'] = $term-&gt;label();


Note: you are in class it's better to inject entity.manager service and change the line \Drupal\taxonomy\Entity\Term::load($tid); with something like:

$this-&gt;entityManager-&gt;getStorage('taxonomy_term')-&gt;load($tid);