Okay, found an online source on how to change that name - you would follow the same steps, just mentally substitute "computer" for every mention of "This PC":
[Tips] Tweak and Customize Windows 8.1 Explorer
I followed these directions up to the point of actually typing in a new name. Since I simply do not trust uSoft or any Windows implementation in situations like this (*), I didn't ACTUALLY change the name though I could have.
Microsoft has changed name of "My Computer" to "This PC" in Windows 8.1. Although its just a change in name but many people don't like this new name and they want to rename it back to Computer or My Computer.
You can actually rename "This PC" to any desired name quickly and very easily. Just follow these simple steps:
1. Open "This PC" window and click on "Up" button present in toolbar. Alternatively you can press "Alt+Up arrow" keys together.
2. It'll open Desktop folder. Now right-click on "This PC" icon and select Rename option. Alternatively you can click on "This PC" icon and press F2 key to rename it.
3. Now type any desired name and press Enter.
That's it. You have renamed "This PC" successfully.
So...YMMV - tread carefully.
(*) IMHO, there is NO reason for there to be multiple entries in the registry with the string "This PC" - since I don't trust uSoft to get things like this right, I would fear that one or more of those locations will not change if I follow the above instructions (though they should), causing unknown maybe-future problems. I've been wrong about such fears before.