You could also say anarcho-Marxist or voluntaryist-Marxist or agorist-Marxist thought.
Commies get a bad rap. And often should. Communism is pretty shit, and pretty much always has been since it forked from socialism. It started out as a just-okay idea, pushed on the world by the elites, etc. And of course it all got corrupted as hell. It's just another totalitarian state system like western capitalism.
People like Richard D. Wolff and Yanis Varoufakis are self-proclaimed Marxist economics professors who study capitalism and communism and do not like them. They have newer ideas about cooperating at the grass roots level - voluntarily and fairly. These ideas include turning (not by force) an existing capitalist business enterprise into a worker directed cooperative to democratize the workplace rather than just be the boss's dictatorship. From privatized interests to community/social/cooperative interests.
RE: Open Borders vs. Closed Borders: A Market Anarchist Perspective