I have a 8 month old male German shepherd, he is has always been aggressive toward my 4 year old granddaughter. He has resently been chasing her down and biting her. Is this just the puppy in him showing his dominance in the pack Hierarchy or something I should be really worried about? 

It’s both and yes, you need to stop the behavior.  Puppies may see small children as litter sets or other puppies, and play roughly with them. Usually we recommend stopping it early. By 8 months, your dog is an adolescent and it’s becoming dangerous. He may also be fearful of her or uncomfortable around her. He needs firm handling. Chasing and nipping at the ankles or legs is misdirected herding behavior. However, it can hurt a person and must be stopped.  How often does he see her?  Is she running when it happens? What do you do when he bites her? Has it broken the skin or is it just nips? Is he on leash or off?  What other training does he have?

Because of his age, I suggest getting a private trainer for a few sessions.  First work with the trainer yourselves. Tell the person the situation.  Then have a session with your granddaughter so you can get an evaluation and learn skills to stop the behavior.  If you had complete control over your dog, your command and presence should be enough to stop him, recall him to you and get him into a sit, down or a place by your side.

It could be a lot of things. I also recommend putting a stop to that asap. Getting a trainer is a good idea. At 8 months he can be pretty dangerous to a small child.

I agree with the others but food for thought. Unless your granddaughter lives with you, there is no need for your dog to interact with her.

There once upon a time was a time when dogs were put up when company came over. True story.

That is a good idea but a dog must be trained to be in a crate, in a room separate from the family or outside alone.

This is a good point. You could just put the dog away whenever she is over. Over time with some separation and interactions not being forced between us, I won over my fair share of ornery dogs when I was a kid. Granted they were adults, not 8 month, and the source of their issues was probably different than your puppies.

Most dogs were accustomed to spending time alone, be it a bedroom, basement or backyard. 

It’s interesting these days. There are people on the other forum who believe you are being a terrible owner and will raise a poor dog if you are working long days while doing so.

They were. Now dogs are fur babies and they can’t be alone.  Mine can because I insist on individual alone time, but they don’t like being separated from company. They think every guest is only here to see them.

Well you are terrible if you work. What are you thinking to have a job and dogs?  When I worked it was usually from home, and my dogs got used to being ignored when I was busy. They got enough time when I wasn’t.