My question is partially motivated by this question. I know that up until early 20th century in Hungarian many (or even most) foreign names were translated. For example this poster from 1864 mentions "Shakespeare Vilmos" (not William Shakespeare). The quotes in this work from a 1837 newspaper about the Texas Revolution mentions Moses Austin as Ásztin Mózes and his son (Stephen) as István. This translation habit was even a plot device in the novel Kőszívű ember fiai when the order came for Eugen von Baradlay, not Baradlay Jenő (although in this case the name was translated into German). I seem to recall that newspapers around the start of World War I still translated names of non-Hungarian politicians. Some translated names even survived into the 21th century (Jules Verne is still known as Verne Gyula, Karl May is still May Károly, Marx and Engels are known as Marx Károly and Engels Frigyes), but generally this habit died out sometime during the first half of the 20th century. Did other languages had similar habit? Did it die out around the same time?
It is still common in many European languages (including Hungarian, it seems) to change the order of names. E.g. in Japanese, Korean, Chinese, Hungarian the family name comes before the given name, but when reading Japanese or Hungarian names (but not Chinese or Korean ones!) in English texts, you will usually see the given name first.
One data point for Germany: if you search for "Jakob Watt" on Google Books, you get German publications from up to the 1850s, and he is almost exclusively referred to as "James Watt" afterwards
Translation of proper names was, however, reasonably common when Russian Germans migrated to Germany in the 1990s, e.g. from Yevgenii to Eugen, or Wladimir to Waldemar. But otherwise it has been rare for quite some time, e.g. you will not find serious publications with "Waldemar Lenin".
Anyway, one should not assume that people are terribly consistent about naming. That is why we have Peter (rather than Pyotr) the Great, but Ivan (rather than John) the Terrible.
I did search for Watt Jakab (the Hungarian version) and was surprised to see the name in this form in a Hungarian lexicon published in the 1890s. Apparently at that time it was still usual to translate the names.
Then I searched for an early 20th century person - "Freud Zsigmond" and found an issue of the Nyugat magazine in 1925 published his memoirs. The neurologist's name was translated, but interestingly in the same issue the name of H.G. Wells was not translated (only misspelled).
This seems to be the theme in the 1920s - some names are translated, some are not, even in the same issue (e.g. an 1926 issue has a poem by "Wilde Oszkár" and a poem by Maxim Gorkij (only transliteration happened, no translation).
In Swedish some translated names like that can be found in older texts, like "Johanna d'Arc" in the 1800s who we later always use her native name Jeanne d'Arc for (in contrast to English where they still use their own version). I have Swedish editions by Alexandre Dumas from 1911 in Sweden where his name is given as "Alexander" on the title page.
Historical foreign monarchs are still written with established Swedish name forms when such exist, like "Ludvig XVI" for French Louis XVI or "Viktor Emanuel III" for Italian Vittorio Emanuele III), but newer ones keep their original names, so the current king of UK is "Charles III" in Sweden as well, and not "Karl III" (and there was a short debate about that in media last year).
I think many (in particular younger) Swedes think this practice is just strange when the original is in English, and they will prefer "William" and "George" over "Vilhelm" and "Georg" for such kings. When the original is a language they don't know it might be different ...