There seems to be many different options here!
My stand is: if you have a clean, usable, repeatable double C, nobody asks any questions. I learned that the double octave always starts with C and that Cb is a source of contention.
For all of you SQUEAKERS out there, figure out what RESONANT means before starting a semantics war.
For those interested, here are some interesting links that back up my post:
Dolmetsch Online - Music Theory Online - Staffs, Clefs & Pitch Notation Frequencies Scientific pitch notation - Wikipedia, the free encyclopedia
Amazing what a minimal amount of googling can produce!