Magento: trying to add Coupon Name to PDF invoice

Question

In basic PDF invoice, on only get discount total, no name in front.

I got as far as to the coupon code showing, using:

if($order->getCouponCode()!=""){
            $this->y -=12;
            $page->drawText('Coupon Used: '.$order->getCouponCode(), 450, $this->y, 'UTF-8');    
        }

but I can't find how to show coupon name.

Also, I use coupon, but also general discount, based on conditions. Those don't have coupon code or description.

In the cart, they are all showing within (). So how can I have that same thing on my PDF invoice.

Can you help?