No you don’t. At the beginning of therapy, it can be very difficult to share personal experiences with a stranger. There’s a reason why we don’t talk about painful emotions and experiences with just anybody. You may have experienced sharing something personal with someone and then regretted having shared that information.
It’s imperative that you trust your therapist not to shame, condemn, look down on, or judge you. So there is usually a period of time where you are getting to know your therapist as safe and trustworthy. Rightly, so, you do not have to share anything that you do not feel comfortable and safe sharing. Hopefully, a warm and caring therapeutic relationship will develop where you feel accepted and safe to work on anything that is burdening you. Having said that, honesty with your therapist is an important aspect of therapy that is encouraged for effective treatment.