New
#11
You could try unchecking "Register this connection’s addresses in DNS"
Chapter 9 - Windows Support for DNS
However, I doubt that will work because what you want is completely pointless. If you are so concerned about what someone might learn from a unidentifiable computer name then stuff it full of random junk. But a computer name is just that, a computer name. If it provides personal information well that is your own fault.
Also, tin foil hats are on sale at K-Mart right now. Better hurry before they run out!