I don't see how this suggested code would solve that notice. $this->data['filter_name'] is itself defined from $filter_name on line 453 of _/catalog/controller/product/search.php_ so it would behave the same. I've only had a quick look though so let me know if I've missed something.

    $this->data['filter_name'] = $filter_name;
    $this->data['filter_category_id'] = $filter_category_id;