From memory, and from the one time I did it about three years ago: they get a letter saying that the DVLA has reason to believe that they are unfit to drive and that they must pass a medical examination in order to keep their licence. I don't believe the letter says that they've been reported.

And to be clear: when I said "anonymously" I meant from the pov of the person being reported. The DVLA requires some basic details of the person making the report, but they're definitely not disclosed to the subject.