Hey BB!
Haven't got time right now to fully research all your questions properly, but I can confirm that the ACCA member Associations from other states have not deviated from the 'Churches' moniker. My main concern would be our possible exclusion from the very Championships that defines us from other SA metro cricket Associations if we were to completely exclude the 'Churches' component of our Association name. This is what makes us so unique, by giving players who want to compete at a higher level, a vehicle to realise those ambitions. I know in the past that the ability to compete at this level has retained players within our Association, as opposed to losing them to Adelaide Turf, for example. There may (??) have been players who've been drawn over to C&CCA because of these opportunities. I'm not sure.
I'm certainly not precious about the name of our Association, and you're 100% right that the church-going contingent within our competition is minimal at best, compared to 30-40yrs ago. My sole concern is detailed above and I'd hate to see us excluded from the Nationals purely over the sake of a name change. On the other hand, I'm not even sure there is a necessity to retain the "Churches" component of our name to ensure ACCA membership.

Maybe something that can be addressed at the next AGM, as I'm sure Tige would know the answer. Indeed, Q4 about attracting teams & clubs from other assocs would need to weigh very heavily in our favour to warrant a name change, but off the top of my head I'm not sure who we'd target.
As for other Churches assocs having the same problems, I know for a fact that retention of players and attracting players to the game of cricket itself is a problem across the country, not just any particular assoc. Sporting participation of youth as a whole in the electronic age is a problem, so I certainly don't believe it is isolated to any particular assoc or state. Also throw in the fact that more people are having to work longer hours to make end meet in this current economic environment, and as such, time for recreational activities suffers. I'm sure you could add other factors with more research..
I also know for a fact that if the teams representing each metro assoc is anything to go by, the talent pool is definitely dwlindling - and it's not a case of "back in my day..."..

That's not to say that there are quality players in each assoc who can't be stuffed playing rep cricket, but this issue would be the same for every assoc. So I think the snapshot of today vs 10yrs ago when we first started playing PDCA is a fair indication - for example. The only reason we have improved in rep metro cricket is the fact that we have been able to get guys like yourself interested in the program, as opposed to 10yrs ago when most players either didn't have the drive to compete at that level, or wanted to only play on Saturdays.
All that said, I applaud your Club for actively thinking about the now and the future of our Association and how we can ensure it continues for many years to come. It certainly warrants discussion and a lot more investigation into the ramifications of a change - positive vs negative.