to pull on a thread in that prev post, there's all sorts of funny nuances to names in translation/localisation, and the norms vary a lot by location as far as I can tell.
sticking to target-language English, the Asterix localisations are generally very well regarded for finding lots of English puns to replace the huge amount of French puns. in this case, the translators prioritised sticking to the spirit of the original names (dorky wordplay) over directly using the French names in English where the joke would be lost. so for example, Asterix's dog is called Idéfix in French after idée fixe, and this is rendered Dogmatix in English, which manages to slip an extra dog pun in there.
but, because of the thorough localisation, it was only when I got older that I found out the broader context of bandes desinées that I'd read as a kid like Asterix or Tintin. as a kid, they were just 'comics', just as Pokémon was 'just a cartoon' that happened to be made in Japan, not an instance of a special thing called 'anime'. but isn't that an interesting quirk? we like to refer to the distinctive creations of xyz region by loanwording their language's name for the whole medium. (following this pattern, Chinese animation is sometimes called donghua, and Korean animation aeni... unfortunately the French for 'animation' is just 'animation' so we can't play that game there.)
but yeah, a similar norm evidently was in effect for American localisations of anime, generally taken to an absurd extent (jelly donuts etc.), but even so there are many cases where it is still uncontroversial. most English-speaking fans of Pokémon will use the localised names they grew up with (so Ash and Charmander, not Satoshi and Hitokage), and the translators still continue to come up with new wordplay for each new batch of puns. if you ever download a fansub of Pokémon which uses the Japanese names, it can be a little jarring at first to relearn the names of the creatures!
however, in most cases nowadays in English translations of CJK media, the current norm is to transliterate the names into the Latin alphabet (using romaji, pinyin or one of several systems for Korean), except maybe to use the native spelling if it's obviously a foreign name in the original, or names that have a very literal meaning (e.g. ヨルハ二号B型 becomes YoRHa No. 2 Type B).
so, in an English-language context I would most often write "Haruhi Suzumiya" and not 涼宮ハルヒ. but even here, we've swapped the name order! it would be less common to write Suzumiya Haruhi in English (the Japanese style where the surname is first), and doing so would sometimes be seen as weebish. (though to be fair, I am not avoiding that if I'm talking about Haruhi in 2025!)
except of course, even just as far as name order, sometimes there are people like Yoko Taro (横尾 太郎) who are usually written lastname firstname in English, which causes no end of confusion to people who try to respectfully refer to him by his surname but call him Taro, which is his personal name. but that just seems to be the way Yoko Taro wanted to be known in English, and the gaming press just kinda went with it. even more confusingly, Yoko Taro's wife (who is known as the artist on the Taiko no Tatsujin series of rhythm games) is more often known as Yukiko Yokoo in English, the opposite order to her husband and a different romanisation of her surname.
however, these norms vary a lot by context. for example it feels more natural for me to write surname-first 'Ushiromiya George' for 右代宮 譲治 than 'George Ushiromiya', because that's the choice that the Umineko-Project translation team made, but this still hides the nuance that George's Western name is written in a really weird way using kanji in the Japanese. I can't think of a way to express that in English that wouldn't be really cumbersome.
another complication is that, even with names transliterated into the Latin alphabet, readers may not be familiar with the source language's phonology and may still end up reading the name differently. for example, when English-language commenters talk about Look Back, they may refer to the character Kyōmoto as 'Ki o mo to' and not 'kʲo mo to' (like the English 'skew'), because that's a more common way to interpret those characters in English.
and of course we can add to that that some languages use the Latin alphabet in a significantly different way than English, so if you've got some Irish characters in your story you'd need to know that Meabh and Siobhan are pronounced /meɪv/ and /ʃɪˈvɔːn/ (that's with the standard English pronunciations which are actually a bit different than the Irish ones...)
as another wrinkle, when fantasy character names are written in a different script for a different phonology (e.g. a character name in katakana), and it's unclear to the translators whether a specific Western name was intended, they just have to guess. For example, a character in Witch Hat Atelier was named アガット Agatto, and I recall reading a scanlation that reasonably assumed this is a gemstone name, 'Agate'. however, the official translation went with 'Agott' for the character's name. did they ask Kamome Shirahama about this and find out this is her preferred romanisation, or did they just make a different choice and interpret it as a fantasy name? I'm not sure, both are plausible.
in general, in names as in other areas, a translator has to be remarkably literate in all the random allusions a source work might throw out, and make a judgement call to what the original work was intending. I kind of love reading translation notes for this reason.
on top of all the above, there is also the fact that many people will have two or more names for different linguistic contexts, because their (say) Chinese name is hard to say for people who speak another language. that is a real aspect of many peoples' experience, which people likely feel all sorts of ways about that we probably want to depict in fiction!
so as ever, in translating something you are constantly making decisions, depending on which aspects of the original work you want to get across, what sort of vibe you want to communicate (e.g. you might want 'visual novel English' if you're translating something really chuuni), how much cultural knowledge can be assumed in your audience, how cumbersome it would be to get across a particular nuance, and so on. the best case is when you have multiple translations, so you can see how multiple people interpret the same source. I don't think anyone wants any more jelly donuts replacing onigiri, but figuring out the best approach for a given context really is where so many interesting questions lie...
