Version: current experimental branch, dedicated server i created my own faction, i build my base, a hover etc. i am able to change the name of the base, but the base stays public. Changes are not saved, neither to private or faction.
Something similar happened to me: I found the "Opportunity" on my Arid Planet, set up Solar Panels, Constructor and Cargo Boxes. I thought I forgot to switch from Public to Private and changed that. Opening CP, flipped from Public to Private, closed CP. Opened CP again - Faction was Public again.
I logged out. Cleaned Cache. Logged in again. Started last Saved Game. Faction stays on Private, as it should be. Switched in CP back and forth but the Faction change sticks and does not switch back by itself.
Finding a similar issue, both @elmo and I are affected (co-op, of course). We create a faction to make sure we can share structures and resources, and the faction displayed in the control panel seems to be incorrect. For all the structures we've built so far, it shows that it's already owned by our faction, when in fact they're actually still Private. We have to set it and then check the HUD marker to make sure our faction abbreviation is at the start.