I'd say that the Aamaniians started switching to 'Aa'-based names a few generations after the Cult Wars ended. While it likely started prior to that among the faithful, it wasn't likely as widespread.

Conversely, I do the opposite with the Zandir. For the first few generations during and after the Cult Wars, they did the whole "all names start with "Z" schtick" but that petered out rapidly. Occasionally, the Sultan would hearken back to the old days and require everyone in the nation to begin their name with a Z and occasionally it is "fashion" for government agents to have their names start with Z, but otherwise the Zandir themselves have names starting with every letter possible (and a few that aren't quite possible too).