Using the prevailing term gets in the way of standing out. Chess.com seeks to stand out. Erik has made that clear: the term sought must be appropriate, but also must be new and distinct. The object is to grab more market share, and even to expand the market itself. Convert more casual players into online correspondence players by drawing them into a catchy name for what old hands always will call correspondence chess.
cChess is catchy, but derivative of iWhatever. eChess is not only derivative, but is the name of a competing site.
asynchronous is precise, but so is the mathematical description of how the knight moves: one square on the square (as a rook) followed by another square diagonally (as a bishop) continuing in the general direction away from the square of origin. It is easier to say that it makes an L shape. Imprecise terms are catchier.
Serial Chess! A new suggestion. The term connotes asynchronous, and might be catchy. Moreover, it marks continuinty with correspondence chess, the form that notorious serial killer Claude Bloodgood used to gain his master rating.
There is no real debate on this issue; clearly, Correspondence Chess is the most viable title, according to the votes and the discussion.
I seriously doubt that a casual player wouldn't know what the word "correspondence" means. If they don't, then how would you except them to understand something like "live chess"? Also, if a person doesn't know, there is a magical thing called Google. Surely it can't take as much time to type "correspondence chess" into Google as it would take to figure one's way around the site after the extremely confusing redesign?