I've heard such pockets called many things, including mail-slot and envelope. I've long known they are organic to Ulster-type coats. However, in their typical execution, they are all right angles--essentially a rectangle with an inset flap just below the top edge.
Apparently, such pockets are a foreign concept to Neapolitans. Maybe I'm wrong about that, but Mariano couldn't make heads or tails of what I was showing him. For a long time, he thought I wanted a flapped patch pocket with double stitching and thick, swelled edges. Those are the sort typical of Rubinacci overcoats. You can see them on bespoke examples posted online as well as on their ready-to-wear overcoats.
Eventually he realized I was asking for something entirely different. That's about when he started complaining that I was trying to get him to make me an English overcoat. Anyway, by the time that conversation was over, I was not sure what I was going to wind up with. He said something to the effect of: "We will find a way to do it our way." I assumed that meant I was likely going to wind up with flapped patch pockets--which are admittedly quite lovely in Rubinacci's execution, so I thought whatever.
But then I got this in the mail:
What I mean about them being bizarre is not that they are done mailslot-style (though this was unexpected by this point), but that the "envelope" is shaped just like a Neapolitan rounded patch pocket. As noted above, all other envelope-style pockets I've seen have been fully rectangular in shape.
Anyway, see what you think. Dopey, as you can observe below, it is not merely a patch pocket with a slot laid over a flapped, welt pocket. Thank God. Rather, the welt and flap are built into the patch (or envelope, whatever) itself. The pocket is hence not built into
the coat, as a welt pocket would be, but over it.