I'd post a screen cap if the Insert Image button here worked like the forum icon implies it should.
I'm semi-pro with software Q&A, so I apolize b/c this is kind of two bugs at once, but I was wondering why there wasn't a clear ID other than color for a selected mining base base, and fidget-clicked the rename area for the base.
So I retried. I seem to be able to rename AI-owned mining bases in beta 1.