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even i have the same problem...
i have pc with 4th gen core i5, intel graphic 4200 processor

Even i got the same problem....
please check the thread link
https://forums.kali.org/showthread.php?25360-KALI-linux-booting-in-half-screen
i described the problem...

did you solve your problem now..
am facing the same problem now...

I have been facing a problem with the view of desktop.

1. The desktop is covered more than a half screen (3/4).
2. I checked for the desktop session initially after first time booting, it is as...

I tried i as you told setting the session-name .
But still it is failed to laod the gnome 3, it is displaying some error liked failed to laod the gnome 3 because you driver is not supporting 3D...