As Shazam (aka Captain Marvel) has been around for close to 80 years, there have been a number of iterations of the character. In at least one major version, we learn that Billy's Captain Marvel identity is a dead ringer for his late father.
In the Power of Shazam! series from the mid 1990s, writer Jerry Ordway identifies Billy's parents as C.C. and Marilyn Batson, a pair of married archeologists who were murdered by Theo Adam, a thug working for the evil Doctor Sivana. As you can see from the image above, C.C. looks pretty much identical to Captain Marvel. Likewise, Marilyn is depicted as looking very much like Mary Marvel, the alter ego of Billy's sister, Mary Batson.
My interpretation of this revelation has always been that Billy would grow up to look just like his father, but that's just conjecture on my part.