Yes, cooked bones are very hard and can be very sharp. It would recommend that you try and feed the dog food with unflavored metamucil in it (1 tbsp. per cup). This will set up like thick jelly in the stomach and may coat the splintered bone so it can pass through easier.
Sometimes thes splinters will scrape the stomach or intestine and cause pain and a very tense belly. Sometimes the bones can become lodged sideways and they have to be surgically removed. I have seen steak bones actually penetrate through the intestine. If he strains to have a bowel movement or if you see any blood, that is serious.
So I would recommend letting your vet check the puppy out as soon as possible.
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Dr. Louis Gotthelf
Animal Hospital of Montgomery
Pet Skin and Ear Clinic