Thanks, the additional info is helpful.
If the peeing isn't huge amounts at any given time marking is a very good possiblity, especially if you've had other dogs in the house. If that is in fact what it is you would need to make sure your supervision is flawless.
You have about a 3 second window to correct a behavior for training purposes. You have to catch him in the act, make it an experience he doesn't care for. Most dogs respond well to an immediate ruckus of noise exclaiming No no no and picking up the dog and immediately taking him outside and praise him heavily (quite opposite from the previous experience of going inside) - of course that's training 101 but you have to be consistent. Any time you aren't witnessing the peeing happen it's too late to correct the behavior once you've found it.
Obviously a 9 month old puppy is going to be decent in size already and picking him/her up might not be feasible so work smart as you know your limitations. You may want to consider having your dog on a leash that you have in your hand and can give a tug correction to this behavior and proceed to lead the dog outside to continue the praise outside where you reinforce the good behavior. I know this is quite a commitment, so use time that you do have available and realize that crate time when you can't focus on the dog is ok.
If it is marking yes neutering can help. You may also want to make an extra effort to clear any old dog scents by cleaning areas that he's paying attention to by sniffing and marking in with an enzyme type deodorizer. I really like Nature's Miracle, but I'm sure there are other options available.
Hope this helps. Keep us posted on the progress.

Sorry so late to see this thread is still going are you still having the same problem?

---

Steve
Dobes are like potato chips, you really can't have just one...