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I have released my P85 for trade in on delivery of a P85D, my Tesla App still shows my old car and VIN #. It can't log in to the car. I also still see my old Model S on My Dashboard.
It shows both and lets you choose the one to view. That is the main reason for the ability to name your Model S, so you don't have to identify each one in your collection by its VIN. (Not that I personally have more than one.)
You can now have several cars on one app. It gives you the option to "choose a car". To get a car removed you have to call Tesla or have your DS email Tesla to remove it from your online profile and phone app.