I think you should also assume it's called "Archive of our own" because of the same sense that Woolf had in "A Room of one's own". This is our space to do our thing, precisely because if it was someone else's space sooner or later they, at least ostensibly for good reasons, prioritize something else over our thing and it's destroyed.

So it's at least not at all a coincidence that AO3's authors are predominantly women. This story of assuming that they can thrive in a shared space and then discovering that, again often for ostensibly good reason, they're not welcome to use it after all, is very familiar to women. Whether you're being thrown out of a cafe for breast feeding ("Nudity, not allowed") or turned down by employers despite having the same skills as successful male candidates ("Bound to have kids and then we'd just have to replace her anyway") it gets wearisome, better to have a place of your own.