I would say contact the local vets and perhaps place an ad, but definitely make sure they have pictures of him or something that can identify him for sure, as some people will try to scam a free Yorkie. If no one claims him and no local vets report a missing Yorkie and you've done your part in trying to help locate the rightful owners, I'd say keep him after that. I don't think it's wrong of you to keep him after doing the above, just my two cents!