The concept of trademarks dates back to master craftsmen putting identifying marks on their work to build up a reputation. Trademark law gives that practice some legal enforcement.
I’m sure you can find some anarchist who would oppose any law, but I’m much more familiar with people who want a small government and wouldn’t mind that government enforcing trademark laws. They also generally support truth in advertising laws or labeling laws (“you should be able to sell anything you want, as long as you tell people what’s in it”), or product liability laws. Those laws make for a better functioning marketplace.
They might argue it’s up to the incumbent to protect its brand, crushing the competition and holding the market under a tight stranglehold. Like the Romans: Ubi solitudinem faciunt, pacem appellant.
I’m sure you can find some anarchist who would oppose any law, but I’m much more familiar with people who want a small government and wouldn’t mind that government enforcing trademark laws. They also generally support truth in advertising laws or labeling laws (“you should be able to sell anything you want, as long as you tell people what’s in it”), or product liability laws. Those laws make for a better functioning marketplace.