General Surgeon. Usually a general surgeon can performs this surgery. I would ask your primary care physician who they recommend. Sometimes this procedure can be done laparoscopically (the surgeon will make a few small incisions and use a camera for the surgery). However, laparoscopic surgery eligibility is determined case by case, depending on the surgeon's clinical judgement and experience, and even insurance.
Surgical Oncologist. There are various reasons to have a gastrectomy. If you are dealing with stomach cancer, there may be advantages to having it done by a surgical oncologist. This type of surgeon has been specifically trained to do the operation to provide the best outcomes for cancer patients. Specifically, surgical oncologists may be able to remove more lymph nodes which could improve odds of survival.