It'll be his wee that's killing off the grass...don't worry, when he starts to **** his leg, all the bare patches will be around the edges...and your srubs and plants.
Sorry, not a lot you can do but follow him around with a watering can & wash the area he's been in, diluting it will help a bit.
I tried the latter, and it didnt work, but it has for some, havnt tried dog rocks, as we opted to have all the lawn removed in favour of slabs!! With just one dog, if you pour a whole bucket of water over the place the dog has urinated, it will dilute it, and will help, but with more than one dog, we found it hard to keep up.
Also can be affected by what he is fed on. If he has complete dried food, then give him half of it soaked, then mix it with the other half. The more liquid he takes on board the more diluted the pee will be.
is it a female ? we had no trouble with our lawn when we had a male puppy grass stayed fine, a coupleof years later we had a female dog and she has ruined the lawn we have big patches, read up on remedies inc "give the dog tomato sauce on all its food" also a lot of remedies contained chemicals which we did not want to give, we just decided we loved the dog more than the grass.
good lck with the puppy training
Dee