Yes, the ovaries (and uterus) are essential for good health our whole lives. You shouldn't need to lose any organs if the cyst is benign. A surgeon with good cystectomy skills should be able to remove just the cyst and send it for frozen section while you are in the operating room. If it's benign, they shouldn't need to remove anything else.
Unfortunately, far too many women lose organs unnecessarily. Only about 10% of hysterectomies and oophorectomies are actually necessary.
How big is the cyst? You've had it for 6 years?