It's important to note that *most* physicians would keep your discussions with him/her private, but "private" does have it's limitations.

I know that most docs do write down most everything you tell them, and herein lies the problem.

Your medical file privacy and access to them is regulated by a set of rules called HIPAA. However so, access to these records is routinely given to insurance companies, MIB (Medical Information Bureau), state/federal agencies, and others under the HIPAA guidelines. In same cases, even your employer can get the records, especially if they are self insured. Insurance companies are notorious for obtaining patient medical records and sharing them with each other.

If you are in a med. marijuana state like California, these details can be accessed a variety of ways, including what you tell your physician.

Read:
Medical Records Privacy

The bottom line is that you NEVER want to give your real name and pay IN CASH at the docs office if you are dealing with anything you want to keep private. If you do use your real name, tell the office staff at the docs office that you refuse to give your SSN# or submit the claim to insurance.