Morkus from Orkus
At least with Adam and He-Man there was a massive physical difference. Sure He-Man might strongly resemble Adam, but resemblance among strangers happens all the time. He-Man had huge bulging muscles that Adam didn't have which would cause people to dismiss thoughts of them being the same person as their imagination. Superman and Clark had the exact same build, height, hair color, eye color, etc. The only difference was a pair of glasses and the clothing.Considering that in the old cartoon Adam and He-man look like the exact same guy in different clothes the mindboggling part is that someone wouldn't know. So basically the same issue than with Superman.
In the new show Adam actually looks significantly different than He-Man, so it makes far more sense.