This is a great question!
PCOS, because of the word "ovary" in its name, is often thought of as a gynecological disorder. However, it has symptoms affecting quite a few organ systems, many of which gynecologists may not be specially trained to treat.
Before you ask for help with your PCOS, be sure you know exactly what it is that you are wanting from that person.
Are you trying to become pregnant? Then a gynecologist is your best bet. Do you have acne or facial hair? A dermatologist is most likely to know the latest and best PCOS-friendly treatment options. Family history of diabetes? Consider a diabetes-specialized endocrinologist. Keep in mind, a specialist is trained to see your condition through a very finely tuned set of lenses, and that means the possible answers they provide will have some bias. Medline published a study a few years ago illustrating this bias, reporting that a gynecologist and an internist would have very different ways of diagnosing--and treating the same PCOS. So it is important to know what your goals are, before choosing the best person to help you reach them.
Despite those recommendations I just gave, consider that you may not actually need a "specialist". Some of the best physicians I've worked with on behalf of clients have simply been good listeners and willing to look for solutions even if they didn't have them, themselves. That person could be a country doctor, if you live in a rural area, or a family practitioner who has been your primary caregiver for a very long time. What matters most is that you get solutions in a respectful fashion!
I am biased because I am a dietitian and not a physician, but I strongly encourage you to find a physician who values a well-trained dietitian as part of your treatment. Nutrition is one of those topics everyone knows a little about. But it is also one of those things a lot of people think they know more about than they really do. I've encountered a lot of nutrition advice for PCOS given by health professionals that actually could have been counterproductive. It is important for each person taking care of you to excel in the part of your treatment they are trained to excel in...but also to refer out to others who excel in their own part of the picture. No one can possibly know everything about everything!
A strong nutrition program can often do the job that medications are prescribed to do. So making extra sure that nutrition and lifestyle are in good order before jumping into medications, surgeries, and treatments, can save a lot of time and frustration. Even if it turns out that medication and other treatments are needed in addition to medications and procedures, you may not need as much medication, and you may have better tolerance for and success with, the treatments your physician provides for you.
On that note, qualified naturopathic physicians and acupuncturists may have treatment options that work well for your individual situation. I have seen several of my own clients do very well with a team that included medical doctors IN ADDITION to specialists in these areas. What made it work, was a willingness on the part of each of these professionals, to work together with the other professionals.
One of the most important responsibilities you have, once you ask for help from a medical professional, is to follow their advice. And to follow it long enough to give it a chance to work. A very common tendency I see, unfortunately, is for a person to try advice, but not long enough for it to actually work. And then they blame the physician. Or, to spend more time on the Internet looking for reasons to NOT follow the doctor's or dietitian's advice than actually giving it a chance in real life. If you are asked to take medication, take it consistently. If you are advised to exercise, then exercise. It is not the physician's fault if the medication s/he prescribed was not used as advised!
Once you've found the person you feel fits you best, remember that a lot of the answers to the syndrome are about changes YOU can make for yourself. Doctors, dietitians, acupuncturists...can guide you toward those changes, but they cannot make them for you. It's important to remember how much of the responsibility for your success comes from other people, and how much of it actually lies within YOU.
