Get categories of queried posts

You need a:

1. array of post id ( ok )
2. array of category id ( not yet )
3. array of category id/name with unique value ( not yet )

using wp_get_posts_categories( $post_id ); returns an array of category id, so you can loop your $ids calling this function to collect all categories id.

with the array of categories id you can set up a brand new one with id/name pair and then with array_unique(); clean up it from duplicated values.

I can’t find any other solution, so:

UPDATE

<?php
/*
 *Loop through your $ids and:
 * get all the categories id for your queried posts ( wp_get_post_categories( $id ) )
 * loop through this new array to get single category data ( get_category( $catid ) )
 * set up a new array with term_id/name value pairs ( $categories )
 * clean up your new array from duplicate values ( array_unique( $categories ) )
 */
foreach( $ids as $id ){
$catids = wp_get_post_categories( $id );
  foreach( $catids as $catid ){
    $category = get_category( $catid );
    $categories[$category->term_id] = $category->name; 
  }
}

$filtered_categories = array_unique($categories);

?>

I’ve tested and now works. Hope it helps!