What is this headset's name per the Standardized Headset Identification System

Yes ZS56/40 - Zero stack with 56 mm bore diameter and 40 mm fork crown race.

It is zero stack because it is a black cup containing the silver bearing, but the bearing ends up inside the frame tube (i.e. not external). The 56.10 mm dimension gives a snug interference fit with a 56 mm head tube ( bore diameter). The 39.95 or so is about the 40 mm dimension that interfaces with the crown race/steerer tube. That last measurement seems slightly tight but possibly measurement error, tolerances aside it would be called a 40 mm.