Since you're asking about the symbol
V: drawn (as it usually is) surrounded in a circle, it is visually very like the anarchists'
A symbol (which is also drawn surrounded in a circle), except upside down.
If you read the original
comic graphic novel rather than the movie, V's anarchy is frequently evident.
Her name is Anarchy. And she has taught me more as a mistress than
you ever did!
She has taught me that justice is meaningless without freedom. She is
honest. She makes no promises and breaks none. Unlike you, Jezebel.
I used to wonder why you could never look me in the eye. Now I know.
So goodbye, dear lady. I would be saddened by our parting even now,
save that you are no longer the woman that I once loved.
Here is a ﬁnal gift. I leave it at your feet.
The ﬂames of freedom. How lovely. How just. Ahh, my precious
Anarchy… “O beauty, ’til now I never knew thee.”
Actually the letter "V" is used in each of the 40-odd chapter titles (starting with The Villain and ending with Valhalla), with other significant appearances as well ("a 'Violet Carson' rose")
V's personal identity is a mystery until the end, so it's not surprising that the 'name' is too.
As for whether it stands for a "group": initially it's the eponymous V who uses it, later (towards the end) the symbol is adopted by members of the public generally: e.g. a schoolgirl draws it on a wall
when the cameras stop working
near the start of Vox Populi chapter. Furthermore,
Did you think to kill me?
There's no flesh or blood within this cloak to kill.
There's only an idea.
Ideas are bulletproof.
Therefore, "V" is a name for an idea.
There's out-of-universe evidence too for the "anarchy" theory. For example in this interview, A FOR ALAN, Pt. 1: The Alan Moore interview, Alan Moore is quoted as saying,
So I decided to use this to political effect by coming up with a projected Fascist state in the near future and setting an anarchist against that. As far I'm concerned, the two poles of politics were not Left Wing or Right Wing. In fact they're just two ways of ordering an industrial society and we're fast moving beyond the industrial societies of the 19th and 20th centuries. It seemed to me the two more absolute extremes were anarchy and fascism. This was one of the things I objected to in the recent film, where it seems to be, from the script that I read, sort of recasting it as current American neo-conservatism vs. current American liberalism. There wasn't a mention of anarchy as far as I could see. The fascism had been completely defanged. I mean, I think that any references to racial purity had been excised, whereas actually, fascists are quite big on racial purity.
So, V (himself) stands for out-and-out anarchy, and the story is (apart from being about love and "letting go") a story of benevolent anarchy overcoming inhumane fascism.
(I suspect there were other out-of-universe reasons too for choosing or discovering "V" but I don't know them).
My personal theory is that, in-universe, V comes from "Valerie" not from "room five": Valerie was the woman in room four, who wrote a letter to the man in room five. I suspect that V might have done what he did, in memory of Valerie.
Valerie wrote the letter, in her own hand, while she lived.
I delivered it to you as it was delivered to me. The words you wept over were those that transformed me, five years earlier.
V... she's beautiful.
Who was she?
She was the woman in room four.
I'm going to give the world what Valerie wanted it to have...
A great abundance of roses.