All neurosurgeons are trained to diagnose and treat anything in the spine. Some orthopedic surgeons take extra training to specialize in spine surgery and they are equally qualified to treat HNP. Some general surgeons have dedicated a lot of their operative time to exposing the spine in cases where the abdomen or blood vessels are dangerously close to the spine and need to be carefully moved out of the way. More recently, pain management doctors have been doing some percutaneous (needle through the skin) procedures, but not having been trained in diagnosis and management of disc problems, they need guidance in decision making on the indications for those procedures.
Personally, I would see a neurosurgeon or an orthopedic surgeon who has been fellowship-trained in spine surgery. Some neurosurgeons have little interest in spine surgery and limit their practice to brain surgery, so that is another consideration when choosing a spine surgeon.