Make your comings and goings from the house nonevents. I don't say anything to my dogs. This has resulted in dogs that think changing clothes is an opportunity to get petted, but I can live with that and they don't give a second thought to being left alone. An immature dog that has unsupervised run of the house is going to get into trouble. This is not a behavior problem, this is a puppy.
Puppy training is entirely different from treating separation anxiety.
If your dog is under 2 years old and you are unsure which problem you are dealing with please give us a call. If your dog is alone longer than eight or nine hours a day I strongly encourage you to get another dog or a cat for company. Living alone is unnatural canine behavior. Wolves are pack animals that live in social groups and are rarely alone. I think most animals are happier when they live with another of their species.