PHP: Show the title of a menu element depending the current category

wp-menu-custom-title-category.php

/* ----------------------------- FUNCTIONS.PHP --------------------------*/

/* @Workether ------------------------------------------------------------
Get Category ID by his name.
--------------------------------------------------------------------------*/

function get_category_id($cat_name){
  $term = get_term_by('name', $cat_name, 'category');
  return $term->term_id;
}

/* ----------------------------- END FUNCTIONS.PHP --------------------------*/

<?php 
 /* @Workether ------------------------------------------------------------
 Get the first current category
 --------------------------------------------------------------------------*/
 	$category = get_the_category();
 ?>

<div id="blog-header">
 <h1>
	<?php 
		$menu_titles = wp_get_nav_menu_items(38); // Get menu ID=38
		$category_ID = get_category_id($category[0]->cat_name); // Get the first category ID via the get_category_id custom function

	   switch ($category_ID)
			{
		case '10':
		      // If the ID is 10, get the first element of the menu
		      $title = $menu_titles[0]->title;
			  echo $title;
		      break;
		case '11':
		 	  // If the ID is 11, get the secont element of the menu
			  $title = $menu_titles[1]->title;
			  echo $title;
		      break;
		case '3':
			  // If the ID is 3, get the third element of the menu
			  $title = $menu_titles[2]->title;
			  echo $title;
		      break;
		 // For every other element not listed above
		default:
			   echo "Latest Posts";
			}
	?>
 </h1>
</div>