Once the bone is removed, the surgeon uses metal plates, screws, and titanium cages to support the spine. This is called spinal fixation with instrumentation. The cages used are round or cylindrical in shape. They can be inserted wherever the disc and/or vertebral bone is removed. This means you shouldn't lose any height after the excision.
Some of this may depend on how many and how much of the bone is removed. Neurosurgeons and plastic surgeons work together to minimize any disfigurement. Often, except for a scar, there is no outward sign that any bone has been removed.
It may be best to make an appointment with your surgeon to discuss the operation. Find out what are your options. Ask about both possible and likely complications or problems that can develop. Make a list of questions so that you don't forget to ask what you want to know before surgery.