OK. I wanted to bring this up:
Now I've made my jokes about "Chad Steven" and how many girls want to have him "shatter" them...if ya know what I mean. (͡° ͜ʖ ͡°)
But in all seriousness, I have started calling it Steven's Fragment or Fragmented form and here's why:
Look at this:
This form gives Steven a HUGE power boost and lets him go all out, but the drawback is that the things that make him human? His morals, compassion, love for others? All of that is broken and "fragmented". His Diamond Heritage is in complete control in that form and he isn't the Steven we all know.
Let's be real: Steven was FAR from himself when he shattered Jasper. And when he came back to his senses, he was devastated when he realized what he had done. The fact that he was sobbing "Please be OK" was proof enough that he never meant to shatter her.
But in that form, he's not in his right frame of mind. He's stronger(even more so than anyone else) but he's also unstable and loses any moral restraint he would normally have.
Pretty much in this form: Anyone can end up like Jasper did, even one of the CGs.
This would have been a cool scene. This is a comic titled "Garnet's Worst Nightmare":
That's how it would have gone. Steven has no moral restraint in that form. Even if the Gems would have tried to use force, Steven still would have won. Know why? Because Jasper wasn't holding back either! And if she lost, what does that say for the CGs?