Can the cause for a potential surgical procedure be kept private? what does it say on the insurance bills about what you had to consult about or have treated?

This might depend on the particular surgery and possible causes of the problem. You'll need to ask the surgeon. However, in the US there are very strict laws designed to prevent disclosure of personal health information (with fines of $5,000 or more) (google HIPAA for more information). You can be confident that friends, family, etc will not learn details you don't want them to know. Good luck.

The actual cause/ diagnosis for surgery may be revealed on the charge issued by the surgical office. That will remain private, but will be issued to the insurance policy owner, such as a parent or spouse, for example, if patient not carrying his/her own policy.