I recently wrote about why I reject the "anarchist" label. Basically, the vast majority of anarchists are hard-core communists, and anarchism is commonly associated with opposition to the free market.
Individualist anarchism has always been the exception to the rule. While anarcho-capitalism is an offshoot of individualist anarchism, it has its roots more in classical liberalism and the Old Right than in the movement of Proudhon and Co. When I do use "anarchism" to describe my beliefs, it will always have "market" or "(neo?) individualist" or something else before it. But to use the word by itself, without any further clarification, is misleading.
"Anarchist" these days is seen as one of 20 leftist sects handing out pamphlets at the Socialist Workers of Eurasia (or whatever) book fair, perhaps at a table next to the Maoists. No thanks.
People would be free to set up "voluntary socialist" institutions in an ancap world, so long as they are voluntary, non-coercive, and based on private property. People would be free to set up capitalistic businesses as well, and those who don't like it can form their syndicates, communes, nudist colonies or whatever. (I don't predict success for any of this leftist quackery, but they're free to give it all a shot.)
The thing is, all these institutions would still have to exist within the general framework of a market economy. Even socialist states have to trade with the outside world and thus deal with markets to some degree. The market can never be abolished entirely. Anarchists--in the common sense of the term-- refuse to understand this, which is why I'm not one.