I suppose so, 顔 does mean face though. And I think in English we also say things like “two-faced” (although typically in a bad way) or like, “a person with many faces” to mean someone who acts different ways in different situations. I feel like the metaphor makes enough sense in translation.
I would argue that the expression is more about outward appearances or societal expectations than it is about a way of thinking though. He has two “faces” - one he shows when he’s a king, and one he shows when he’s a hero. It’s about how other people see him. There probably is a better way to translate it that gets around the implications of the phrase “two-faced” in English but imo using “mind” is kind of changing the meaning. Also to me at least, “two faces” and “two-faced” don’t quite come across as the same thing, as one is a metaphor and the other is a set expression.