Can my health insurance provider tell the primary account holder that I am under about any medical conditions?

• no medical life insurance
• life insurance no medical exam
• private medical insurance
• insurance doctor
• pregnancy health insurance

I am in my early twenties and just found out that I am pregnant. I will be graduating from my university in December and I am not ready to tell anyone in my family until I graduate. Can my insurance provider contact my parents (the primary account that I am under) about my condition, the tests being run, or any of the medical costs if I am over 18 and covering my medical costs?

Additional Details

I am talking about the insurance provider, not the doctor. Since they are the primary account holders for the insurance I didn't know if that meant they had a right to know about any costs or if they would be notified about the amount that I am responsible for paying, or if the insurance providers are only allowed to speak with me regardless of who is the primary holder of the account.

Thank you for your answers everyone. I am actually further along in my pregnancy than I thought and will be going over my medical cost obligation after the doctor contacts my insurance on November 27 (the day I find out the sex). So far I have only had three tests done (blood work, papsmear, and an ultrasound at my first visit a month ago) and haven't had anymore tests. I graduate the 14 of December so it was close anyway. Thanks again for all the helpful answers.

Can my health insurance provider tell the primary account holder that I am under about any medical conditions?