Yes! One important point to make about communication with any psychologist is that psychologists are bound both by law and, for American Psychological Association members like myself, by a code of ethical conduct for the profession to keep information that is shared confidential. On a personal level, most psychologists take this responsibility very seriously.
There are a few exceptions where law does require psychologists to share some information from therapy. One of the most important is that, if a client makes statements that present a credible threat either to harm him/herself or to harm another person, the psychologist is of course bound to take necessary steps to ensure safety. In most cases related to harming oneself, the psychologist is going to work with the client to find a way to ensure safety without breaking confidentiality. While psychologists of course do want to keep people safe and alive, it is also true that we want the client to feel in control of that process as much as is possible.
Another exception is that psychologists are “mandated reporters.” This means that, if a person shares information about child abuse or about the abuse of an elder or dependent adult, the psychologist does have to report that information to appropriate authorities.
In addition, there also are a few cases where a judge might order a psychologist to share some confidential information. The psychologist will “claim privilege” and not provide information in these cases until the judge orders him or her to do so.