What are the family going to go by as adults? I don't see Freddy being Captain Marvel Jr since they are are unlikely to call Billy Captain Marvel. And I don't see Mary being Mary Marvel.
This was never really resolved in the new52 reboot of the team, or rather maybe Geoff Johns and Garry Frank never fully thought out what Mary, Freddy and the new Lieutenants; Eugene, Darla and Pedro call themselves when transformed? Pedro asks- Are we "Shazams too!?"
Freddy suggests wanting to be "King Shazam", so maybe they were going to go by chess designations: King, Queen, Bishop, Knight, Rook?
Although they are not using Marvel, there is no reason they can't still keep Captain, and by extension expand on the others with Military rank designations.
Billy would obviously still be Captain. The others like the traditional Lieutenants have different added ranks.
Another suggestion was going by referencing their respective Deity acronym Namesakes: Hercules, Zeus, Mercury, etc..
Or simply their respective power attributes: Wisdom, Strength, Courage, Power, Stamina, Speed.
Or like Power-Rangers their colors: Shazam-Green, Shazam-Blue, Shazam-Red etc.
In the end when transformed, they end up just using their personal names, among each-other.
How that if overheard affects their secret ID...?