Nicholas and his children in order of birth, 1910
The daughters of the ruler of All the Russias couldn't be called princesses. There were princesses all over Europe. For those priviledged women who could call the tsar their daddy, the only title that would do was Великая Княжна, "Grand Princess." Today it is most accepted as Grand Duchess. Children of emporers, rather than mere kings and queens, were often called by a loftier title. In Austria the children of the Emporer were archdukes and archduchesses. In Russia, they were grand dukes and grand duchesses, indicating that they were "imperial highnesses," instead of "royal highnesses."
As the family continued to multiply at a very quick rate, Alexander III (Anastasia's grandfather) decided in 1885 that only children and grandchildren of the tsar would be grand dukes and grand duchesses. The remainder were referred to as princesses. Only in Russia would being called a princess be a downgrade.
And despite the grandiose titles, the Romanov children were still commonly referred to by their first names and patronyms, going so far as to rebuke the servants for calling them anything else.