Prince Willem-Alexander was called Alexander. His own father litterally said during the registration in 1967: "His names are Willem-Alexander Claus Georg Ferdinand. We call him: Alexander."
When Prince Willem-Alexander registered his daughter in 2003, he stated: "Her names are Catharina-Amalia, with an hyphen like in my name, Beatrix Carmen Victoria". In contrary to his father, he did not say what her calling name was.
Despite the calling name "Alexander", the regnal name became Willem-Alexander. "That is my name.", the Prince said in an interview.
The State Information Agency (RVD) stated: "Zodra de Prins van Oranje de troon bestijgt, is zijn oudste kind, Hare Koninklijke Hoogheid Prinses Catharina-Amalia, de eerste in lijn en daarmee de troonopvolger. Zij is vanaf dat moment de Prinses van Oranje."
("Once the Prince of Orange ascends the throne, his oldest child, Her Royal Highness Princess Catharina-Amalia, is the first in line and thus the heir to the throne. From that moment she is the Princess of Orange")
The pertinent use of the double name in communications is -for me- an indication that she will be known as Her Majesty Catharina-Amalia Beatrix Carmen Victoria, by the grace of God Queen of the Netherlands, Princess of Orange-Nassau, Etc., Etc,. Etc.