There are, broadly, three options for dealing with real-world etymology in-universe. Which one works best depends on the table and the specific circumstances.
Forget translation: everything is interpreted, including this very conversation!
Just because you're talking about a real-world word's etymology from Greek through German by way of Latin on the way to being absorbed by French doesn't mean that your character is. In-world, your character is giving a similar description of how the word started in Draconic then found its way into High Dwarvish then into Low Dwarvish (which is the form used for commerce, of course) and thus into the common tongue.
Everything is translated; etymology is out the window.
Everything that the players say and hear is translated. Translations almost of necessity strip the benefits of knowing a word's etymology (and of knowing related/root languages).
In this scenario, the GM should generally make sure that all (relevant) players are using the same meaning of the word, to avoid confusion, but the etymology is irrelevant except insofar as it can help the player understand something.
If in-game etymology is needed (eg., to solve a puzzle), the GM needs to provide it to the players (at least, the players who would reasonably know it).
Etymology is (magically) preserved.
"Because magic", it happens to be the case that etymology matches well enough between worlds that it's relevant.
It could be that fantasy languages map one-to-one with real-world languages (eg., Elvish is French, Dwarvish is German, and Common is English), and thus etymology comes along for the ride.
While the exact quirks of history that brought this specific word from Primordial through Dwarven into Elvish and then Common (ie., Latin through German into French and then English), something close enough happened that the etymology lines up.
Proper nouns getting de-proper-noun-ized (eg., the "romance" in "romance languages" seems ultimately to derive from Rome) just implies that a similarly-important person/place/thing existed (or event happened).
So, your character isn't explaining the word's Greek etymology, but how it got from its Draconic roots to Common.
Languages don't map.
If that strains credulity, then consider that the translator between the fantasy languages and your native tongue considered etymology when choosing how to translate.
It's rare for two languages to have a perfect one-to-one mapping of words, doubly so for those words to have the exact same shades of meaning. Sure, it's almost a certainty that every language has a way of referring to "the person currently speaking" (that is, "I" or "me" in English), but it needn't be a single word - in fact, there's no particular reason that it has to be a simple concept to relay! So, when translating, the translator takes cultural information into account when selecting the right word or phrase. This translator also takes etymology into account, adding just the right shading to the translation.
Consider the difference between "I ate a sandwich earlier" and "at some unknown point in the past, though likely since the sun crested the horizon, the person who was going to become the one who is currently speaking happened to be in proximity to a loaf of bread, some sliced meats and cheese, and a tomato; they, being hungry, assembled the aforementioned ingredients such that two slices of bread contained the others then ingested the resulting meal". Technically, both sentences convey the same information. The latter sentence is, generously, a bit unwieldy, but it's not such a stretch to think that a non-human mind would see its precision as worth the extra words and time. But, we're humans and such circumlocutions are typically employed to obfuscate the speaker's intended message. A canny translator, then, would recognize that the Fey princess was speaking as plainly as possible, so the best interpretation for the human listener is "I ate a sandwich earlier".
My experience is that the first option - interpretation over translation - is almost always preferable. Trying to keep track of which real languages map to which in-game languages is an exercise in frustration and can bring unforeseen and undesirable connotations (not to mention uncomfortable attempts at faking an accent). And, as Glazius mentioned, the list of eponyms is surprisingly long; assuming that any world will have a history compatible with Earth's historical quirks so that etymology remains even remotely consistent is ... well, let's just say that suspension of disbelief has its limits.
Really, though, it's usually best, IME, to ignore linguistic quirks, etymology, and even the logic of wordplay, rhyme, and meter, when translating between in-world and real-world languages. Riddles should rarely translate neatly, and poetry almost never (puns are right out). Just accept that you're playing a game, and that it's more fun when you can - on occasion - reason out a riddle in the real world rather than simply throwing a die roll at some gibberish to see if your character can figure it out.