I started out calling this the Tommy John Twist because that is what it is most often associated with.
Tommy John surgery.
Typically, it first gets a pitcher's elbow and then gets their shoulder.
That's exactly what happened to Matt Harvey, Alex Reyes, and a number of other pitchers.
However, I'm now trying to figure out what to call it because I'm seeing more and more pitchers who have shoulder problems without first having elbow problems, and that includes Zach Davies of the Brewers.
What's worse, there also seems to be an association with Thoracic Outlet Syndrome, such that I also refer to this as the Thoracic Outlet Syndrome Twist (TOS-Twist).