Actually, the current change in his name is story specific. (assuming that Day of Vengence is still valid in the reboot universe)
Shazam (the godlike mage who gave Captain Marvel his powers) was killed by the Spectre. Billy Batson had to become the new Shazam to ensure that the lineage of magical protectors continued. Mary Marvel is still Mary Marvel (or at least she was prior to the reboot and GOD, please tell me if they retconned all this crap that they undid all the shit they did with her through Infinite Crisis), Captain Marvel Jr is still Captain Marvel Jr, etc...
Again, this is based of the original continuity, as stated before I haven't followed jack since the reboot.
Eh, just wiki'd the new Captain Marvel post reboot and he got completely reset, so apparently none of that stuff happened.
This is another reason that the reboot pisses me off. Some of the best work DC comics had done in decades is just down the drain. Almost everything surrounding 52 was just great, IMO. Hell, they managed to make freakin' Catman and Ragdoll into compelling characters.
All that... GONE.
Yeah, man, fuck the reboot and fuck DC.