Well, kbin seems to have gotten its name from a longer form, "karabin" (see the - defunct - polish devlog URL referenced here: https://karab.in/m/karabinDevlog/wpisy). I have no idea what it means, but it could be Polish (though - according to Google translate - "kara" is "penalty" and "karabin" is "rifle", and I don't think that's the theme the dev was going for, so maybe it was a portmanteau that I just won't get as a native English speaker).
As for mbin, it was forked from kbin by a guy named Melroy, so I'm betting that's where the M came from.