This has happened to me recently - listed an item of clothing and got a good price for it. However, when I was packing it, I noticed that it was ripped at the bottom- I emailed the buyer and in the end, I refunded her the sale price and sent her the item as she was going to have a bash at repairing it. She left me brilliant feedback. I think most people are very reasonable and nice if you are upfront and honest.
The name written on the Woody doesn't sound that bad to me if the toy is in otherwise good nick. I would offer a choice: either a full refund and not send her the item at all or send her the item and give her half her money back.