It still happens with kings, queens and popes (for example, Elizabeth II is called Isabel II in portuguese and spanish), but before it seem to happen with literaly everybody.
A famous example: portuguese explorer Fernão de Magalhães is called Ferdinand Magellan in english and Fernando de Magallanes in spanish. Jules Verne is called Júlio Verne in portuguese.
When did this stopped happening?
I don't have an explanation for you but maybe I can ask a related question in this thread based on an observation. I speak German and Italian and was exposed to the media of both countries, so this is what this is based on.
There seems to be a "cut off person" for these translations at least when you look at the British royals.
In Italy Queen Elizabeth and Prince Charles are referred to as Elisabetta and Carlo but the sons of Charles are referred to by their English names William and Harry, and not by their Italian names Guglielmo and Enrico. So the cut off appears to be Charles.
In Germany King George IV and Queen Elizabeth II are usually referred to as Georg and Elisabeth but Charles is referred to as Charles and not Karl. So the cut off appears to be Elizabeth.
I was wondering if this appears to be the rule with these kind of translations. Are there specific persons who appear to be the last bearer of a translated name and starting with the next generation the translation is gone?