00-register-taxonomy.php

<?php

register_taxonomy(
  'acme-category',
  $postType,
  [
      'label' => 'Acme Categories',
      'rewrite' => ['slug' => 'acme-category'],
      'capabilities' => [
          'manage_terms' => 'manage_options',
          'edit_terms' => 'manage_options',
          'delete_terms' => 'manage_options',
          'assign_terms' => 'manage_options',
      ],
      'hierarchical' => true,
  ]
);

01-wp-insert-term.php

<?php

$termInfo = wp_insert_term(
  $customPost->getName(),
  'acme-category',
  ['slug' => sanitize_title_with_dashes($customPost->getName())]
);

02-get-term-by.php

<?php

$parentTermInfo = get_term_by(
  'term_taxonomy_id',
  $termInfo['term_taxonomy_id'],
  'acme-category',
  ARRAY_A
);

04-wp-set-object-terms.php

<?php

wp_set_object_terms(
  $customPost->getId(),
  [
      $parentTermInfo['parent'],
      $termInfo['term_id'],
  ],
  'acme-category',
  true
);