What makes princess Leia a princess?

_In the rough draft of A New Hope, Leia was roughly 13 – 15-year-old princess (the same age as Padmé Amidala in Star Wars Episode I: The Phantom Menace), the spoiled daughter of King Kayos and Queen Breha of Aquilae. In that draft, she had two brothers, Biggs and Windy, whose identities were substantially revised into their current form by the fourth draft (though they did not appear in intervening versions).[12] The later story synopsis established her as Leia Antilles, the daughter of Bail Antilles from the peaceful world of Organa Major. In the fourth draft the names were turned around so that Leia Organa came instead from Alderaan.[13] Source

It isn’t until Episode VI (movie) that she discovers the truth about her true heritage. Is it the same in the books?

Even then, I don’t recall her ever claiming to be a princess. It was always a title bestowed by others.

The Organa family who adopted her were royalty

It’s the buns…

The sciptwriters, to put it bluntly :)

The attitude.