Add the following PHP code to your child theme functions.php file.

//to display the category on the admin order page
function action_woocommerce_admin_order_item_headers(  ) 
{ ?>
 <th class="item sortable" colspan="2" data-sort="string-ins"><?php _e( 'Item category', 'woocommerce' ); ?></th>
 <?php 
}; 
// define the woocommerce_admin_order_item_values callback
function action_woocommerce_admin_order_item_values( $_product, $item, $item_id ) 
{ ?>
 <td class="name" colspan="2" >
  <?php
  $termsp = get_the_terms( $_product->get_id(), 'product_cat' );
  if(!empty($termsp)){
  foreach ($termsp as $term) {
   $_categoryid = $term->term_id;
   if( $term = get_term_by( 'id', $_categoryid, 'product_cat' ) ){
   echo $term->name .', ';
   }
  } } ?>
 </td>
<?php
}; 
// add the action
add_action( 'woocommerce_admin_order_item_values', 'action_woocommerce_admin_order_item_values', 10, 3 );
add_action( 'woocommerce_admin_order_item_headers', 'action_woocommerce_admin_order_item_headers', 10, 0 );