what's the term for a coin's obverse and reverse rotational orientation. For example, when a coin's design turns upside down when turned (such as on U.S. coins), and when design stays right side up for both sides when rotated (such as with British and Canadian coins)?
Alignment.
Coin alignment (when design turns upside down when turned) or medal alignment (when design stays right side up for both sides when turned).
On every coin page (f.i. https://en.numista.com/catalogue/pieces46260.html) you can see on the right hand side the features of that coin type. The bottom line, there will be the alignment, in case of the example "coin alignment ↑↓".