Back in the first game, you'll recall that the viruses had actual names (or code names) which were usually shortened to a single letter - however by RE2 the code name seemed to vanish and the letter didn't seem to refer to anything. Now in RE6, the code name idea returns:
T-Virus = Tyrant Virus C-Virus = Chrysalid Virus
So what does G stand for in G-Virus (from Resident Evil 2, the virus that gives Sherry Birkin her super regenerative powers), were we ever told anywhere?
The resident evil wiki said many believe it's called the "gene" virus but no solid information or conformation was ever given.
That doesn't sound very plausible since all the RE viruses infect the host at a genetic level, so I'm more inclined to believe the God answer. It fits like a glove, since a God is what Birkin wanted to become after he was shot by UBCS troops to become all-powerful and get revenge.
Still, if there's no official canon answer then it could be either really :)