My best “new” idea thus far is:

Hyperdata

I see your reasoning behind selecting this name, that it's more descriptive of its benefits than datasphere etc, and has a "clear statement of utility". I don't know, there's something about it that appears reminiscent of the nineties somehow; I immediately thought of hypertext. I'm not saying I dislike it, but I'm wondering if it has the potential of a wider appeal beyond those with a more technical appreciation.

I think that when/if you come across "the" name you'll know it straight off in a way you haven't with previous ones. And it will still seem good in a week or a month's time.

I’m brainstorming site names and trying to think of one that conveys that divergent opinions are not censored. Also still trying to capture the concept of escaping from the creeping totalitarianism. Also wanting to stand out (be memorable) from the crowd of vanilla site names. I am also interested in the theme of technologically crashing through borders and barriers. I would like to capture the notion of a permanent archive with no dead links forming in the future.

OK, I'll put my own head above the parapet now and suggest this one: Immute. Shortened from "Immutable". Permanent, and also implying not to mute opinion, standing up to oppression, and can't disappear down the memory hole.

Though I concede it doesn't also fit with your wanting to

capture the open data notion that everything (not encrypted nor marked with copyright) is editable and there can exist multiple versions of any document — everything can be forked.

Could this be comparable with an evolutionary tree , or Phylogenetic tree?

P.S. I also like the debate.org concept for an app, wherein two debaters go against each other and everyone else is allowed to post comments.

EDIT:
Which reminded me of this game of Cambodian chess shown here (up to 15:45), which I believe is called Makruk. How the bystanders are contributing ideas to the confrontation.