Personally I would really love a clearer separation between WordPress and WordPress.com. Ideally the names would be more different, but that's not easy to do something about.

Splitting the apps would be a great idea, but then I feel the functionality for self-hosted sites without Jetpack would have to be improved. At the current time, I believe you cannot do much more than create/edit posts and pages.

Also, the Calypso-based desktop app is called WordPress.com, so it would be logical for the mobile apps to be called the same thing.