How come Princess Leia is a princess?

OK, a Star Wars question asked by my hubby... how come Princess Leia is a princess? Who is the king and who is the queen? Her stepdad was Senator Organa. Her real dad was an ex-slave turned dark lord of Sith and her real mum briefly served as Queen of Naboo; akin to a presidential term. Plus, if 'princess' is intended as an acknowledgement of her royal origin (her mum) then isn't this a bit counter-intuitive given that the whole aim was to hide her birth from her real dad (Darth Vader)?

Yeah, I guess I'm a nerd.