I am not a native speaker in the english language, but what about "state boundaries" as the term for these borders?
Regarding the second part of your question, this OSM Boundaries Map might help you to get the existing boundaries from the OSM dataset.
With regard to your requirement to only have one polygon per state:
There is the concept of exclaves and enclaves, which is not that uncommon all over the world. Please see the wikipedia page for a good explanation. Since using a bounding box of the state is also not an option in your use case, I honestly don't see how you can handle that issue (in a good, professional way) without having multiple polygons per state. Maybe you can name them differently, something like e.g. Kentucky1, Kentucky2, etc., where in the end the additional number can be ignored?
On the other hand, I somehow hope, that the mentioned GPS vendor is already aware of the enclave/exclave problem, otherwise I would probably talk to them again and discuss together a possible solution.