I think in this scenario it looks fine as the given name, きもひめ (remember the ひめ part can be translated as a proper name and still pass, like Momohime or Torahime. Her status can be explained in passing or, as with some games, is simply unimportant and enough people playing the translation will already get that, tbh. That said, the novels for Tengai Makyou Ziria actually did translate the names of the characters into English (i.e. Princess Virgin Snow), and those games are very similar in time/setting. How you choose to do it in the end is really up to you. Both have their advantages/disadvantages and in both people who play translated JRPGs may already have enough recognition for why this is to not really mind.
In my opinion, I think the safest thing to do (especially in a retro game where you might not have infinite space for character names to be used over and over again) is to simply throw in an extra sentence or throw in three words that simply explain the pun when revealed. If that doesn't happen, throwing in an extra Translator's Notes document along with the translation might be best.