One researcher has seen "communication" in one species of octopus, but it's mostly looking big and dark to drive away others, or small and light before being driven away[0]. It's a very primitive communication, like rattlesnakes do to scare away dangers. Not the kind of complex system I was thinking of.
I'm being very human-centric, though. It just seems like if they're intelligent enough to recognize individual faces, use tools, and learn from what other octopi do, a complex language would be inevitable. And from there they'd accrue oral histories and localized cultures.
Their reproduction strategy would have to change, when you produce 100,000 eggs and die taking care of them there’s not much chance to develop culture.
I highly recommend the Netflix documentary ’My Octopus Teacher‘. This is the story of a photographer diving everyday for a year, and developing a two way bond with an octopus.
