Hmm, I say just stick with "correspondence chess" as the time controls of 1 move per day or more is similar to a correspondence time control.
I still don't know why there is such big controversy over the name. I will still play the chess no matter what it is called 
Correspondence Chess would definitely be a wrong term since Correspondence Chess plays by different policies and by using that term one would (or could) assume that using books and databases is encouraged.
The term, Email Chess, doesn't make sense and also gives wrong impressions.
Turn-based is the current acceptable nomenclature for chess played as it is here. Other than using that term, I would think you would have to create your own name, such as i-Chess, as Cotter suggested, or e-Chess or sometimes y-Chess or Web-Chess or move-and-wait Chess.
"A-move-a-day chess"
MADchess?
I think we should send an email notification after every move. Therefore reinforcing the name email chess.... NOT.
However, some of the games are not one move per day so the title could be misleading.
All I am doing is shooting down ideas, I'm sorry. I have no better name for it than anyone else.
I think we should just assign each name we want it to be called to a number on a dice and just let it roll. The fate of chess.com will rest with one number (or just the e-mail/correspondence/madchess/turn-based/dead/OTC(over the computer)/online chess part).
Ok. I admit it. Email Chess is not the right name. But what IS?? Help!
Most other chess sites do either LIVE chess, or correspondence/turn-based/email chess, so they don't have to differentiate.
Please help!?!?!