Yes. You can trust that anything you tell me will be kept strictly confidential. I will not share any details of our coaching sessions with anyone. Not your relatives, not your employer, or anyone else. To do so would be a violation of my own ethics as well as those of the International Coaching Federation, of which I am a member.
The only time I would break confidentiality is in the event that you tell me that you are planning to kill yourself or hurt someone else, or if I were subpoenaed by a court. In these situations, I would communicate my concerns to the appropriate authorities or provide any information required by law.