Someone has some good speculation on the meaning of the name here:
"But then to take it further, the actual name of the product. The 'Index'. If you search the patent you will find extensive references and discussion of "index of refraction", which means "measurement of the bending of a ray of light when passing from one medium into another.". Kind of neatly ties in the logo and the product name, doesn't it?"
^Valve has a patent on a lens set up to utilize smaller screens for a larger FOV.
Some people were wondering how they could manage such a large FOV, with how small the headset is.
As you can see in the above image (in the OP as well), that Valve is using physical IPD. One of the few things that we know for sure about the headset.
The speculation is that the resolution will be about par with the HTC Vive Pro.
So the aversion to 3 is real the Valve index logo is 2 semi circles and a full circle, they couldn't bring themselves to have 3 semi circles also notice at the bottom only 2 controllers not 3.