Get custom taxonomy name (not the term) in custom post

I have found an hopefully elegant solution

$taxonomy_names = get_object_taxonomies( $post, 'objects' );
foreach ($taxonomy_names as $tax) {
    if ($tax->query_var != 'tag') { 
    // needed because $taxonomy names containes more than one query_var
        $current_tax_name_slug = $tax->query_var;
    }
}

This one works for me