Outing is appropriate in this and similar contexts: [Person or Media Outlet] outed [person, usually well-known]. This usage connotes negative or mixed motives unless "outed" is preceded by accidentally, inadvertently, etc., or the context is fully within a trusted LGBTQ-friendly environment where such a revelation is unlikely to have negative repercussions. Until relatively recently, and to this day in many settings, it was a grave personal breach to tell Person B that Person A was any variety of LGBTQ without Person A's express, particular consent. In the late 1980s my mother asked me whether I would consent to her revealing to a relative who had just come out to her that I'm a lesbian. She was right to ask, although in that instance I had no hesitation in telling her to go ahead. That did not feel like being outed; the request for permission and my willing consent made the difference. In settings and with persons for whom the revelation is no big deal, far more common now than 25 years ago, the appropriate expression is simply," Person C told Person B that Person A is gay/lesbian/bi/trans/queer/LGBTQ." But I would still ask if I were at all unsure about possible repercussions.
The reflexive use is much less common, at least when meant sincerely: generally used with accidentally, etc, and rarely without modification.