As far as I understand, in a practical sense "red prince" is just a trait unique to the red prince character (who also has other more generic traits). So it sounds like you're really just talking about traits.
Did you mean you want to write your own flavour/background text for your custom character? I don't see any reason why they wouldn't let you do this. It should be easy, but it also doesn't seem very important.
Or are you hoping for something like XCOM 2 or the Sims, where you can build your own character with a backstory and upload him to the Steam Workshop?
