"Sleeping Beauty" is a fairy tale adapted from two separate versions of the same story: the Charles Perrault and Brothers Grimm tales. In Perrault, the princess's name is Aurora; in Grimm, it's Briar Rose. Both names now are used for her depending upon the part of the story, but most people know the princess as Princess Aurora.
Princess Aurora is the daughter of King Stefan and his Queen. Aurora was betrothed since her birth to King Hubert's son, Phillip, but something goes awry right away. At the celebration of her birth, Aurora was blessed by two of the three good fairies with the gifts of beauty and song. So far, so good.
However, as the third gift is being given, the evil fairy Maleficent arrives in a fury. She was ignored when the invitations were sent out. As her revenge, Maleficent curses Aurora with death by the pricking of her finger, by the time the sun sets on her 16th birthday.
The three good fairies are unable to dispel the curse, but can lessen its effect. Fairy Merryweather makes it so that in the event Aurora ever does prick her finger, she would not die but instead fall into a timeless slumber, until her true love comes to awaken her.
King Stefan orders all spindles in the kingdom destroyed to prevent Aurora from pricking her finger, and he also sends her into exile in the forest to hide from her enemy Maleficent. It is at this point that she takes the name "Briar Rose."
However, Maleficent is not called the Mistress of all Evil for nothing! Maleficent tricks Aurora into pricking herself, and Aurora is laid in state at King Stefan's castle. Prince Phillip comes to her her, defeating Maleficent and breaking the spell. Through the power of true love, Prince Phillip and Princess Aurora bring together their kingdoms and live happily ever after.
When Walt Disney decided to make "Sleeping Beauty" in 1959, he resolved not to choose between the names for the princess, but instead to use both. Thus, the princess is born 'Aurora,' but she later takes on Briar Rose to go incognito when she hides out from the evil spirit Maleficent.