Trademarks are a government-enforced (i.e. publicly-mandated) monopoly, which is fundamentally antithetical to capitalism.

Capitalism: "an economic and political system in which a country's trade and industry are controlled by private owners for profit."

For sure, there are many shades of grey to be had here, and the world has 0 purely capitalist societies (in fact, such a society is inherently impossible). But every time the public controls trade and industry, e.g. when enforcing trademark law, that isn't capitalism.