I always thought it should be called USRT when strictly synchronous, but indeed, everyone else called it USART, so I called it the "USART controller"
For instance, this is the code I use to emulate it (also includes pin connection list in the comments): https://gitlab.com/higan/higan/blob/master/higan/sfc/control...
(Seems silly to emulate this device, but it allows for testing and debugging the code you want to run on real hardware.)