Names are a nuisance, especially for auxlangers. Consider the following:
Petrus Peter Pietro Pedro Pierre Pyotr
What do they have in common? They all begin with "p" and have an "r" further on. If we increase the level of abstraction, we can add more. But from a practical standpoint, what do you call someone whose name derives from Greek Petros?
Natlangs have trouble with this too, and there is no single answer. Do you translate the name—"Pedro" in Spanish, "Pyotr" in Russian, and so on—or simply reproduce the original? The original is more likely most of the time, but it may create problems: How do you write (or pronounce) "Shakespeare" in Esperanto, for example? Do you write it as in English, with perhaps the pronunciation in parentheses? And which pronunciation? The British themselves don't pronounce the "r," at least not in the Esperanto fashion, yet Ŝekspiro is common enough. In Inlis I'd use Shekspia, I suppose.
Anyway, the modern, somewhat smug answer seems to be, "Just use the original form."
What if the original form is obscure or problematic? Do we use "India" or "Bharat," for example? "Bharat" is well-known in its own area, but among the target demographic so is "India" (or anyway "Indi-"), and without the troubling "bh-" sequence. It's good to honor the local name and pronunciation, but it's only ethically required, I think, if we mean to replace the original: if the goal is to supplant the languages of India, we may as well retain "Bharat" as an epitaph. But if we work to leave the original languages in place, it's not so pressing.
You can also see this in the Bible. Zamenhof retained more Hebraic forms a lot of the time. Thus "Isaiah" (a wonderfully variable name anyway) becomes "Jesaja," and "Judah" becomes "Jehuda." (Yes, I know: this assumes an English standpoint. Guess what language we're using right now.) And then there's the matter of YHWH, however you want to pronounce it.
About all you can do is try to find a rule or guideline you can follow consistently. I'll give an example next time.