Black Adam has always had an identity problem. This goes all the way back to 1945 when he debuted as a villain and then evolved into a hero as time went on. The comic book creative team fell in love with the dubious character, much like Magneto and The Punisher, that were treated similarly storywise.
Adam is part of the Shazam family but many may not notice this, other than the costume, without any guest stars from the previous comedy Shazam! Instead, viewers are introduced to new characters in the Justice Society which piggybacks off of The Suicide Squad.