I agree that there isn’t really anything to hide behind. Back in Death Valley Junction (11 miles east) there are free porta-potties across the street from the Amargosa Opera House that anyone can use.

Not much to hide behind over there. Pretty exposed. But there is not many folks to hide from...

I’ve seen a few people camping in tents there. Not too many private areas, although you might be able to rig a tarp as a screen. It’s a big place, and people tend to be pretty spread out, so privacy shouldn’t be an issue.

If you're just in an SUV, you could drive to the top of the hill there and get a nice private spot. You shouldn't have any issues.

SUV's would be fine there, but if you use a tent,the ground is really hard and probably difficult to get tent stakes in. If you sleep in the car, the concrete pad would be fine. You might consider bringing a bucket type potty with lid/bags etc. that you can set up behind a tarp or the vehicle, which you can then dump at your next stop. Not much privacy there, but also not full of people, so a quick drivearound should provide a spot.