You won't need to log out of the Desktop App, all you'll need to do is log in to the Web Client of the 2nd extension and provision it as you did for the first. It will overwrite the first and you'll notice that the Desktop App is now logged in as the 2nd extension. You can confirm this by clicking on the user icon on the top left.
Currently you have an extension logged in to the Desktop App, to change it, log in to the Web Client of the extension you want logged in, and provision it.