I....didn't think this was even a thing. Back then everything that was trying to be cool had an X in it. The brand is great and everything, but Microsoft has always been awful in the naming department, and they picked the most unoriginal thing they could at the time. The Direct X thing might be a part of it too, but if so I don't think there's much more to it than that.

Pretty much, this.

DirectX box. After Sony refused to uae Direct X for the PlayStation.

I always thought that Microsoft was simply aping the PlayStation brand. Seriously, look at the Dual Shock controller and you'll see an X, a square (box), a circle (360) and a triangle (trinity / delta - which really should have been the name for the One)

Pretty much every other answer got it right.

Plus it used to make porn videos before its gaming career.

Because I made it. You know, when I was a toddler.

DirectX Box is a boring story, I prefer the one where they stole thhe name from the PS controller, that one even works out for the 360 and if they had called the X1 the Xbox 1080 then it would have worked for that as well.

Drat, my secret is out!

It was right in front of us this whole time and we never realized.  

Because it's a reference to Microsoft's api, DirectX, in 1999, Microsoft's prototype console used to call DirectX box.