No need for a hyphen in anarchy
Anarchy is a political philosophy, which answers the question of “what is the role of government” with the answer “nothing”. If you have no government, there is no scope for disagreeing about what the non-existent government should do.
There will still be plenty of disagreement about what should happen in society. Some people might choose to join socialist communes, or religious communities, or trading towns, or live as hermits, or whatever other options you can imagine. We can pontificate about what trends might be popular and we can argue about which community will be best… but these are not discussions of political philosophy. They are the equivalent of arguing about the best way a baker should bake bread. The beauty of anarchy is if we disagree about how to live, we can simply go our separate ways and voluntarily join different communities (or bakeries).
Therefore, hyphenated-anarchy is unnecessary. Whether a person self-describes as anarcho-communist, anarcho-syndicalist, anarcho-capitalist, anarcho-monarchist, etc… as long as the person actually is an anarchist, then these are not differences of political philosophy. They might describe personal preferences or predictions about the future, but they do not describe a disagreement about the role of government.
It is reasonable for an anarchist to say that they want to live in a voluntary socialist commune without for-profit businesses. To each their own. We could also debate the possibility that such communities might be (or become) quite popular. Anarchists in the communist tradition should be free to live in voluntary communes and encourage others to voluntarily join them. But it is internally inconsistent for an anarchist to advocate a “ban” on for-profit business outside of their community. Without government, there is no institution to do the banning. While a communist might not personally like business, in an anarchist system they would have to tolerate voluntary acts of trade between consenting adults.
The generous interpretation of anarcho-communism is that over time people will voluntarily stop dealing with businesses and will shift to civil society including non-profits, community groups, clubs, cooperatives, mutual societies, etc. It is theoretically possible that every single person on earth might voluntarily do that. Personally, I suspect that some people will still want to interact with and through businesses, but that is just my opinion. Actually, I think that over time (as society became richer) more people would shift away from business and into civil society. Perhaps that makes me a semi-Marxist?
Either way — under anarchy these are not outcomes to be designed, but rather to be observed as the natural consequence of voluntary interactions. As long as anarcho-communists are just stating a preference or prediction about the future, then they are simply “anarchists” without need for a hyphen. If they are advocating for an organisation with the power to ban things and force outcomes that they like, then they are advocating for a government and they are not anarchists at all.
On the other side of the coin we have anarcho-capitalists who imagine a world with businesses, profit, trade, and all the trappings of a market economy. A standard an-cap vision of anarchy includes competing security businesses which deal with competing private courts to provide a private law system. That is certainly one possibility. But once again, as long as they would tolerate alternative voluntary systems then they are simply “anarchists” without need for a hyphen.