The purpose of states is to restrict access to capital, to protect private property claims. Trademarks aren't even physical things you can claim as property, they're legal fictions trying to enclose culture the same way we have enclosed the land. By your reasoning owning a plot of land, or a factory or a stack of money is a government-granted monopoly and as such inherently not capitalistic.
Plots of land are physical things you can claim as property. Stacks of money are government creations in a sense, but I don't believe that without government creating fiat money, there would be no such thing as money.
And how do you claim as property a plot of land larger than you can patrol and guard yourself in a day? You can't. That's why enclosure is a fairly recent development historically speaking.
I'd recommend reading Debt: The First 5,000 Years by David Graeber if you want
to understand how debt, money and states interconnect. I'm not saying you can't have money without states, I'm saying states are mechanisms to grant and enforce monopolies (i.e. exclusive access to and control of resources). If you want to maintain these systems without states, you'd end up with something resembling feudalism, which is just a more direct way to enforce property claims through violence.