I previously suggested iMobile without knowing that it was already suggested by someone on another blog, so I am pulling that suggestion from the table and replacing it with:

iWorld

Apple is going for the wholly integrated digital life approach, so the name should be something that reflects that. They want to present the ease of use of their .Mac services, such as blogging, posting websites, sharing media, mail, and address book/calendar sync.

iWorld, your world at your fingertips, wherever you go.

I don't know if we are supposed to make multiple suggestions, but my other suggestion would be:

iConnect.

It would carry the same concept as iWorld, but be a bit more direct in what it does.