(It's a more general question, too, is John Juan when he's in Mexico?)
For the biblical Jesus, the situation is even worse. His name was probably originally יֵשׁוּעַ, and should therefore have been Yeshua to us users of the modern day Latin alphabet. But instead his name was adapted to Greek linguistic conventions as Ἰησοῦς (Iēsoûs), and from there transliterated into Jesus.
And then people wrote the texts that would become the New Testament in Greek, because it was the dominant language around the Eastern Mediterranean.
Although it's not quite that simple because the original version of Cyrillic actually has a bunch of extraneous letters that are there solely to represent the distinctions in Greek; in some cases, distinctions that were themselves historical in Greek by that time even. For example, three letters for /i/: I (corresponding to iota), И (corresponding to eta), and Ѵ (corresponding to upsilon), all of which were already pronounced the same in contemporary Greek, and this carried over to Slavic languages as well.
In other cases the distinction became nativized though. E.g. Greek theta, already pronounced as /θ/ in Greek, became the Cyrillic Ѳ - but the closest they could get to pronounce it was [f], and so it came to have the same meaning as Ф, and eventually Ѳ was just dropped as unneeded. Thus e.g. transliteration of Matthew is Матфей, and a bunch of other words where most European languages have "t" or "th" sounds have "ф" in East Slavic languages: e.g. "arithmetic" is "арифметика". But then some words were borrowed into Russian from Latin as well, or from other languages that borrowed them via Latin, and so sometimes theta became /t/: "mathematics" - "математика".
Egyptian mythology would like a word with you. Specially the part where Isis created a snake to bite Ra so that she could learn his true name. But yea, adapting names to foreign languages was a normal thing until recently.
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1. Or maybe the Vetus Latina, I can’t claim enough authority over early Biblical translations to say with any certainty. And perhaps some other non-Western translation would have priority in making the Joshua/Jesus distinction.
2. My grand strategy for making these sorts of cross-lingual comparisons is to use the “other projects” links from Wikipedia which is also a great way of getting more accurate translations for somewhat niche terminology than machine translation or dictionaries can offer.