My puppy has accidents when nervous...?

Your dog has a behavior problem often called submissive urination or excitement urination and probably nervous urination, too. Neutering will not help this. You need the help of a certified applied animal behaviorist (ask your vet for help) or this will be a lifelong problem. You need to rule out the possibility of a urinary tract infection before starting with a behaviorist, so see your vet and ask for help with this behavior problem. many vets have a background in solving behavior problems or can refer you to a CAAB.