This plant was given to me and I don't know what it is. My puppy likes to snack on it and I am hoping it is not dangerous to him.
It's a spiderwort (Tradescantia spp, maybe a S. virginiana cultivar). A quick google search indicates it may cause temporary skin or oral irritation in some dogs, but nothing serious. If your puppy has been snacking on it with no ill effects then it's probably not too dangerous.