I have published several papers and have done a number of peer-reviews (on request by the journals) as well. In the communication with these journals, I frequently get addressed as "Dr. Lastname", although I have not finished my PhD yet.
I don't mind when this happens in predatory requests from shady journals and conferences (science spam), because I don't expect them to do their due diligence in finding out correct personal info on all the people they send these requests to.
But coming from more serious sources it feels weird.
In the beginning, I made the effort to correct them, but as it started to happen more and more, I stopped, but always wonder if this is not misrepresenting myself. Maybe the requests for e.g. peer-review would not have been sent to me if they knew that I didn't have my doctorate yet, as several journals I know only invite PhD-holders to review.
So should I always clarify my status, or is this a pretty common thing happening to many researchers, and no one really cares?