Adding to what @AndrlCh said, "crimson lotus fan" is just one of the possible interpretations of the original Japanese PA name of "グレンテッセン". Seeing the "グレン" part as "紅蓮" (scarlet lotus or just mean the red color of fire) is pretty common understanding I suppose, but some sees that part as "愚連" (rogue, hooligans). For the latter part, as you mentioned fan, I suppose that comes from an opinion to see "テッセン" as "鉄扇" (iron fan). But there's another opinion to see it as a flower name (テッセン、鉄線、鉄仙). See (https://ja.wikipedia.org/wiki/テッセン) for details.
Anyway, as the devs decided to give Katana PAs new names on NA, sticking to Japanese PA names is rather pointless, I feel.