It isn't that simple, is it? Even if you place the black surface on a spacer (adding mass, might I add), the black surface itself is going to radiate heat back onto the satellite via blackbody radiation. This is always going to create a worse thermal situation unless you can somehow radiate away as much heat as you could with reflections. To see what I mean, check out JWST's thermal shield.
E is the Earth. 1 is a thin lightweight black disc to block the view of the rest of the satellite. 3 is the working parts of the satellite. 2 are mirrors to direct any emissions from 1 in the direction of 3 out to the sides and to direct any emissions from 3 in the direction of 1 out to sides.
Consider a shaped charge. It seems wild to me that you can direct an explosion with various shapes of the explosive. Perhaps a similar idea can apply to the blackbody radiation - get it to radiate mostly away from the satellite.
Also, the black part will be pointed at the Earth, not the Sun.
Not sure what geometry you're thinking of. Whatever idea it is, you're stuck dealing with Kirchoff's law, which says optical emissivity and absorptivity are the same number at any given wavelength. I.e., you can't create "one-way trap doors" for heat flow—that would be a Maxwell's demon. Stacking multiple surfaces isn't a way to circumvent this.
If it's just an asymmetric shape, with different material surfaces pointed in different directions, than that of course is permitted.
Kirchoff's law doesn't say which direction it emits in. As shaped charges can alter the direction of where the blast wave goes, I suspect an analogous behavior of a heat shield can direct where the emissions go. I.e. as you say, an asymmetric shape.
V-groove radiators are a really neat, unintuitive design, which gets strong directionality out of thermal radiation. It's the thermal design SPHEREX went with—the space telescope that went up a few weeks ago, that was all over HN.
That's: a cavity that's a thin wedge in between two slightly angled plates, where the interior surface coating is partly emissive, and partly infrared-reflective—it can reflect the thermal radiation it emits. That means specular reflections, following geometric optics, so it works like a horn for light—beams it out the sides in a narrow cone.
It's likely that military satellites used a bunch of tricks to hide itself. But I don't know how useful they are these days. All major space powers have radars powerful enough to easily pick them out. They're needed for satellite collision avoidance analysis.
Also, the black surface only needs to be on the Earth facing side.