Typically, insurance companies require that your therapist provide and share with them a diagnosis for your condition in order to authorize the session. This diagnosis will come from the Diagnostic and Statistical Manual version 5 (DSM 5) which contains all of the psychiatric diagnosis currently recognized. Once this information has been provided to them, the therapist and patient have very limited power over how the insurance company will use this information.
While the insurance company does have legal and ethical privacy standards that they are required to uphold, the laws are unclear and it is hard to know what becomes of the information. Some more severe diagnosis such as Major Depressive
Disorder and others have been known to make purchasing life insurance difficult or impossible and also to in some cases impact security screenings and some forms of employment.
Insurance companies also periodically choose to audit the notes of therapists. This is not designed to impose on your privacy but rather to ensure that the therapist is keeping notes and following procedures in accordance with the requirements of the insurance carrier. While it is not meant to be a violation of your privacy, it certainly can feel like that.