Users on 4chan are by default anonymous when posting content or comments (replies to content). At least when I last spent time there (in early 2007) it was considered a faux pas to post content with a username as it is looked as if one is trying to gain notoriety/fame for themselves, instead of giving up their content for the great good that is Anonymous.
Anonymous (capitalized) is, generally speaking, not a coherent group in any sense, but a meme describing the swarm of memes and the users who propagate them (often first at 4chan) through the internet (a meta-meme?).