Ugh...No "Arabella" was the title of a sad, sad, Italian soap opera I used to see when a teen.
And yes, I agree. They would have christened the girl with a Danish name. The fact her mother is (or was) Australian could not be important. Almost always, in the Royal couples, one of them was foreign, but this was not a pretext to name the Royal children with names of another root than the one of the adopted country of the father or the mother. For example: Alix of Hesse was of German origine, with a British breed (her grandmother was Queen Victoria), and married a Nicholas, the Tsar of all the Russias. Well, their children were named: Olga, Tatiana, María, Anastasia and Alexei...All four names were Russian. Princess Dagmar was Danish, but after marrying the Tsar Alexander III all her children wore Russian names: Nicholas, Georgy, Xenia, Olga and Mikhail..and so on...Of course, we can christen the children with names of another culture inspiration, but the translation must be from the country his father/mother is ruling and in which they were also born: for example, Queen Sofía of Spain christened her elder girl as Elena (who is the perfect translation of "from Greece") , but it is a name very common in most of European countries , and the other two children were named as Cristina and Felipe, very common also in Spanish nobility.
And the examples could go, and go...
Vanesa.