I guess that hat would depend on the country. In Sweden the Bernadottes, in their attempts to seem more Swedish, had a tradition of adapting the names of royal brides. Examples of this are Désirée --> Desideria, Joséphine --> Josefina, Louise --> Lovisa, Sibylle --> Sibylla.
The Swedish Princess Lovisa on the other hand had her name changed to Louise when she married the future King Frederik VIII of Denmark.
Princess Jelena of Montenegro became Elena when she married Victor Emmanuel III of Italy.