In a game called Pathfinder, featuring the accolades of a group of adventurers called the Pathfinder Society, and an organized play campaign called Pathfinder Society, I would recommend against having a skill called Society.
I just imagine trying to google potential uses of the Society skill in Pathfinder, and getting absolutely buried in hits about the lore of the organization Pathfinder Society, or the rules set forth for the organized play Pathfinder Society campaign.
So Culture? Civilization? Community?
What other names for the skill do people like, or is Society the right one after all?
Its Levels all over again! Although I don't play Pathfinder Society, that does sound like it wouldn't be all that clear for everyone who does. maybe culture? I am not sure. I feel like society fits best, but those other things also named society are much less able to change.
Society.
Culture, civilization and community all imply its about a specific one.