Ya me han contestado. Por si a alguien le interesa:
The Name in the Session List in Whatsapp is the Name of the (internal) Application - In this case WhatsWatch (Jessunka2). You can check this by logging in web.whatsapp.com.
Technically it is just a word i'm giving Whatsapp for your Session. So the Session IS OPENED by your device and privacy is no problem 
It is possible to have multiple Sessions opened for WhatsappWeb. You don't have to close the WhatsWatch Session before logging in web.whatsapp.com. Technically it is not possible to "fake" your Scan, sorry.
If you still have problems to use both without getting kicked out of WhatsWatch - answer me. I will check it.
I've already submitted a new Version with better UI and intuitive workflow for better experience. It will be available within 1 week (Samsung is checking every version...)