Matching slug terms from one array to those in array of WP_Term objects to output term names

Perhaps array_map ?

This will give you an array of term names which matched your slugs in $active_filters:

$matched_terms = array_map(function($term) use ($active_filters){
    if(in_array($term->slug, $active_filters)){
        return $term->name;
    }
    else{
        return false;
    }

}, $tax_terms);


//remove the empty array elements which came from terms which didn't match a slug
$matched_terms = array_filter($matched_terms);