Is it possible to register my app to receive Google+ push notifications?
As I understand it, apps are identified by their package name to make sure the correct application gets sent the notification. Would it be possible to get Android to notify my own app that something happened on Google+ by changing the package name? Or is there an easier way? Does Google even want 3rd party apps that build on G+?
It is not possible for 3rd party applications to receive Google+ push notifications. Please file a new feature request on the issue tracker here: http://code.google.com/p/google-plus-platform/issues/entry
If you're interested in the Google+ APIs (which provides read-only access to public data) you will want to visit https://developers.google.com/+/api/.