Historically it's more common than not. E.g. most names of European monarchs are translated.

Popes too. Pope John Paul II was Jan Pawel II in his native Poland, Giovanni Paolo in Italy, and so forth. Pope Francis is Francesco in Italian and Francisco in his native Spanish.

If a Pope has one most proper name, it would have to be his name in Latin: Ioannes Paulus II, Benedictus XVI, Franciscus.

Certainly.

I was recently reading a Spanish newspaper that referred to Queen Elizabeth II and Prince Harry as Isabel and Enrique.

It was a little surprising since I’ve only ever seen the Spanish kings referred to as Juan Carlos and Felipe in English-language media, never by translations.