When I did this sketch last year (inspired by observing last night), seeing was so good I actually tried to see if the companion's rings could be seen crossing into and within the primary's first minimum. Not sure that's possible (due to the laws of diffraction), but seeing was calm enough to give it a look see. I failed to see it.
One thing that was interesting was the companion appeared to be "stretched," almost elliptical, along the primary's diffraction ring. The pair is not equally bright with the companion noticeably dimmer.
The thing that struck me about 32 Ori is it really gave the impression of a cosmic diamond ring. If it needs a moniker, it's "The Diamond Ring Double" for sure.
Edit: larger image.