I'm not sure I understand the paragraph you wrote, but let me try

It varies from language to language, but there are ways of tracing things back. Of course, the easiest way is if things are spelled out in script for us, because then we can read it; although that may be made a bit more difficult depending on the script itself. Let's start with something simple enough like Ramesses in Greek, since you mentioned that: Ραμσής. This is very straight forward to read by itself, as Greek letters have Latin approximates: Ramsēs. It gets harder when you have to read it from Egyptian (transliterated): rꜥ-ms-sw. As you can see, there are no vowels in the script itself, so we have to work backwards with the spoken language to be able to generate something more comprehensible in, say, English. The way this was done was to slowly work back as far as possible with the development of the language. When Egyptian was being decyphered, a significant part of it was done by working back through Coptic, which is a language descended from Egyptian. By seeing how the Copts would speak and spell, we can see some patterns for how to pronounce the words and which vowels would be used, and then you can try to "fill in the blanks", so to speak, which could look something like this: Rīʿa-məsī-sū. Having this, it can either be adopted as is or be localised. Not all languages have all phonemes, so they will often be localised.

But that said, we can't always know for certain, or it may vary, so we can't always just point to a single answer and call it a day. A famous example of how the spellings can vary is seen in the Hebrew spelling of God's name: יהוה‎ (transliterated as: Yhwh). Again, the script doesn't have vowels (y works as a consonant), so some digging must be done (and has been done by people much smarter than I). To sum it up extremely shortly, we see manuscripts, where some could interpret it to be read as Jehovah, while most scholars today agree that it was most likely Yahweh; but arguments exist(ed) for both spellings.

We also have some examples of knowing the rough spelling, though not necessarily the actual meaning. An example of this can be the Golden Horns found in Denmark. On the top of the second of the pair of horns was a runic inscription that has been transliterated thusly: Ek HlewagastR HoltingaR horna tawiðo. While there seems to be consensus that at least HlewagastR is a proper name, there is discussion on how to localise/translate it, with suggestions such as Lægæst (based on the etymology of the first part of the name), Liutgast (a figure in Germanic legends), or maybe it was a collective way of naming the people of the settlement (again etymology based). There is also debate on whether or not HoltingaR is even a proper name at all.

In the cases of languages with only sparse or no writing, it relies almost entirely on backtracking, which can lead to different results depending on the language or dialect being used as the basis. Take for example the Slavic deity Chernobog. Since we don't have anything written down by the Slavs of the time, we rely on how the speakers would say it, which obviously varied. That is why we see spellings such as Czarnobóg in Poland, Černoboh in Czechia, or Чернобог (Chernobog) in Russia. But looking at the similarities in the different descendant languages, the ways it is pronounced, and the patterns of languages change, you can still make a good informed choice when suggesting the root word/name.

(If any proper linguists drop by, feel free to expand and/or correct this. This is just what I have gathered, when casually reading and discussing with some)