different countries use different terms for their royalty. Thea is a Prince because there is no princess title in her country. That is non negotiable.
Picking gendered terms only relate to how the your player character wishes to express their gender. While the title for the MC can be edited by the player, the MC canonically does not inherit the title of Prince/Princess because their rank and status comes from their mother, not their father, and they are not a child of the current Emperess.