Using your word of power as your super-hero name is not exactly a good idea and a powerful magician would probably find a way to hack into it and steal the powers. The wizard may be a powerful magician, but he practices ancient magic and probably isn't familiar with things like techno-magic and stuff, and it isn't always about power, but how something works. They'll probably have to use a spell to make everyone forget the word Shazam which those who are enhanced by the power of Shazam are immune to.
The Thunder Family
Billy Batson = Captain Thunder (A name that's been around since the 70's and Marvel doesn't own.)
Mary Bromfield = Lady Thunder
Frederick Freeman = Commander Thunder
Darla Dudley = Miss Thunder
Eugene Choi = Lieutenant Thunder
Pedro Peña = Mister Thunder
While Billy's dad, being the oldest, would probably be called Admiral Thunder.
This would probably give a classical feeling to it when Billy was Captain Marvel and the family was called the Marvel family and Shazam was just a magic word.
I would like that. Unfortunately it will probably never happen.