What will be the name of the upcoming iPhone app so I know what to search on the iTunes store?

Although, I'm sure there will be fanfare on the site anyway when it is approved!

bump

When you click play on the top left you will see it in the middle..

or just click this link -- http://www.chess.com/play/iphone.html and on the top will be the "Download App from Itunes"

Also i believe the APP will be called Chess.com 

When does it launch?

From this posting it appears to take Apple approximately 2 weeks to review an app: http://forums.macrumors.com/showthread.php?t=568686

I am looking forward to the app.  The screen shots look good.