The place I sent my parrot to when he passed puts a numbered metal tag on each pet before they go in and the tag stays with the ashes. They also did a foot impression and sent the ashes back in a simple but lovely clay urn. It was a little weird seeing the ashes in a ziplock inside the urn but I totally get it since they were a small family business.
If you are able to get it I highly recommend Viva Pinata Pocket Paradise. It’s very chill and easy to pick up and put down. I still play my copy from time to time.