Plant Seeds in Fertile Soil
We use two different kinds of words these days. We use descriptors and names. "Automobile" is a descriptor. "Car" is a name. We want a descriptor which has positive, or at the very least, non-negative implications. In absence of such a descriptor, it's better to use a name.
Libertarian was a pretty good descriptor, but has recently become a name. And that name has become associated with the Libertarian Party and the huge number of people who call themselves libertarians have no principle or consistency. They advocate one tax because it eliminates another, and advocate gay marriage frequently without considering the possibility of abolishing state marriage. So it has implications that we want to avoid; it is no longer consistent in the public mind with our goals.
Panarchy is one possible descriptor. It does have the drawbacks of being a word nobody has heard of before, and being impossible to explain without leading them to think you actually mean "anarchy".
Acracy is also unintuitive and impossible to explain without saying "no government".
But I think I've found a good descriptor.
"Market government" is a contradiction in terms, the two are completely at odds, which invalidates the "government" part while not retaining that appearance. But consider the implications of saying "Market Government" to someone you're trying to convert. They'll think you're a little fringe, which you are, anarchism isn't mainstream no matter what you call it, but their minds are not reflexively closed to the idea. It takes the immediate burden off of proving that we are better off without government (as well as setting aside such considerations as "what about the roads/what about the poor/what about my favorite program) and shifts it to allowing you to explain that you believe government services should be provided by the market, offering you a choice of governments and allowing you to choose the best government for yourself.
This allows you to lead people into the idea rather than the usual response to anarchism, which is to distance oneself as much as possible and criticize it from afar, not bothering to check the validity of any points but rejecting them outright and then seeking a way to dismiss them as patently absurd without needing to actually refute them.
You do not need to tell them that roads, police, and courts may be provided by three seperate companies. If they ask about that, you could say "If the market supports that kind of service division, it does so because that is how the customers want it." This way you can advocate a totally free market without government controls. If they ask "Who governs the government services?" ask a similar question which applies to the present day such as "Who governs the United States?" The obvious answer to either is "the people", although people's power over governments would be much greater with a free-market government than with a central monopoly government.
I'd like to see anarcho-capitalism marketed as "market government" to see if people are truly more responsive and acceptant of the ideas. Showing someone the ideas from the inside before telling them what they're looking at will make it so that even if they quickly figure out that you are advocating anarchism, they will have seen the reasons behind the idea from the inside. This is a good way to deal with the problem of people judging ideas by their labels.
Anarcho-capitalists and libertarians, once realizing the basic truths of anarchism, rarely change and become republicans or democrats. They may abandon the term anarchy, but they do not abandon the ideas. You can show someone the ideas, and if their mind is open, they may never fully abandon those ideas, even if the reject the name given to them.
If you can show them why the market works and why the monopolies do not, it is easy to advocate anarchism under the title "Market Government" and get a number of curious interested people introduced to the basic premises of anarchism before they reject it. It performs the critical function of planting the seeds of truth, which, if nurtured, grow and become stronger until a metaphorical tree of knowledge is planted in them, which they will have a hard time denying if you continue to ask them about it from time to time.
Plow the dirt, get their mind ready for the ideas. If you don't have an open mind, you can only plant in barren land.
Then sow the seeds. Introduce them to the fundamental principles like market vs government, and explain the advantages of the market.
Then water the seeds by citing how the ideas work in various specific instances. Why they are protected from their neighbor advocating shariah law, for instance.
The seed will grow roots into their mind, and become almost impossible to uproot to replace with another tree. Hack as they may at the branches, they might never pull up the roots.
And eventually, if the tree grows large enough, the ideas may spread when the tree bears fruit and plants it's own seeds later on.