Unfortunately even "the name of the machine" can change; e.g., I can invoke the 
shell command "hostname garfield" to change my machine's name to garfield. 
Also, I expect that if Emacs has its process migrated (LinuxPMI, anybody?) it 
will then be running on a different machine with a different name.

How about the attached patch?  The idea is that (system-name) actually inquires 
for the current system name, and system-name caches the result.  If an Emacs 
lisp program assigns to system-name, though, it's no longer updated thereafter.