hi Éric, perhaps you already know, using a characteristic gives you the option of notifying your app of a change, this means you avoid polling.
The idea of using the advertising name as a trigger may very well work (our app looks for a specific device name in the advertising) but is not how it is intended to work.
As to power consumption, advertising means that the bean sends information every... well 20ms or thereabouts (I forget the specifics, please correct me). If instead you use a characteristic then the advertising stops because you are now connected to only one device. Then the amount of polling you use will determine how many messages are sent. If you use Notify, then only value changes are sent (no polling from the app) and then you decide the frequency at which the app gets updates on the sensors.
Characteristics is the way to go.
Bean scratch is also very interesting. You can find information here https://punchthrough.com/bean/docs/guides/features/scratch-chars/