According to Kluge (Etymologisches Wörterbuch der deutschen Sprache, 2019; s.v. x-beliebig) the use of x, y, z by Descartes' (C17) resembles earlier scripture, in which the placeholder had already looked like x, from a shorthand for Italian co, cosa in place of Arabic schai "thing, something". A preference for the available Latin characters is a bare necessity since the commodization of the type press, after all. In this view one might argue that /ɛks/ is an (unetymological) spelling pronounciation not unlike denoting "opening bracket" or "quote" in dictation.
That's possibly too reductive. Phono-semantic matching of ex and cosa has to be considered, at least, giving the question a wider scope:
- Is 'x' the written form of the spoken sound [ɛks], which in turn is a spoken name for the symbol 〈x〉, which is the written form of the spoken sound /ɛks/, which was--probably--not derived from the name of the Latin letter 〈x〉?
The Anlaut is remarkable!
e-, ie-, je- are commonly fused prefixes in German (and English, cp. ever), thus something like ?eks may be expected. In this view it would be reasonable to assume an unwritten tradition that antedates the change to using 〈x〉.
There are for example High German etwas pron. "something", adv. "somewhat", jeglich adv. "any" (cp. each), and je "each" in use as a determiner like French per and á (somewhat uncommon in English, one vote each ~ per person). The analysis is difficult because of the shortness and ubiquity of such particles (thus Grimm, DWB: je) and the reconstruction is to some extent undecided (e.g. Proto-Germanic *ju, cf. Althochdeutsches Etymologisches Wörterbuch: jū).
The syntax and semantics of mathematical definitions and other formal propositions make liberal use of these:
- Each of Peter's friends either likes to dance or likes to go to the beach (or both) ~ for every x that is a member of X, P applies to x or Q applies to x (en.wikipedia.org: Quantifier (logic)), Each had a different solution to the problem (cf. dictionary.com: each pronoun).
More over, French chaque, chaqun "each, each one", "someone" < cha(s)cun seems to be derived from a distributive sense of Greek kata (un) and conflated with Latin quisque (FEW: cata), thence VLat. *cascunum (en.wiktionary.org: chaque). On the other hand, Italian cosa, French chose "thing" may be generally derived from Latin causa, further origin unknown. However, one might legitimately ask per cosa, per què, pour quoi "how so, for what?".
The significance of *-ga- is far from clear in fossilized contractions such as each < *aina-galīk (etymonline.com), jeglich < iogi(h)welīh (dwds.de), either < ǣgther < ǣgehwæther < *aiwō-gikhwatharaz (John Ayto, Word Origins (2005 2e)). As a prefix, it would leave the trailing **-s to be explained.
- a) In the case of etwas, Middle High German indef. pron. ichts vel sim. seems to be genetive of iht, icht in the phrase ichts iht, which further contracted to ichtesit, ichsit, after iht was contracted from earlier io-wiht, iowicht etc., cp. Modern High German nichts "nothing" (Lexer, BMZ, DWB, Schweizer Idiotikon)
the problem being, wiht is without etymology (cf. Kroonen for comparison). Middle High German ne was beside etwas, regional einwas, as well as Proto-Slavic *ničьto (cp. Niederlausitz Besser Ischten als Nischten, Deutsches Sprichwörter-Lexicon von Karl Friedrich Wilhelm Wander: Ichtsen) do rather point to a wh-word (PIE *kw-), whereas Latin necubi is just wrong (Latin.SE: What's up with 'ubī'?).
Relatedly, Lexer knows ixlich as variant to ieteslich (q.v.): "aus ie eteslich, ie etelich mit einmischung von iegelich: jeder." (viz. anyone)
- b) This is convincing as a soundshift because there is also ôt, eht (Lexer, BMZ) from ekkhorôdo, ekrôdo, ecchert (Wackernagel, Althochdeutsches Handwörterbuch), cp. ettlich, early modern High German adv. conj. echt "nur" (cf. DWB: ächt and Pfeifer: etlich, oder; they agree only with a Gothic conjunction). Another example seems to be onomatopoeic and so much less convincing, cp. ix, iks (Rheinisch, NB: "Dat stammt noch von Icksnilijes Zeiden Bernk. —"; Swiss, Palatinian; Luxemburgisch) for ätsch (dwds; LWB and Idiotikon suggest synchronic variants with itz, uz).
Anyway, eht (b) is distinguished from icht and etwas (a) because of vowellength, it seems, but this should be chalked up to regional variation in time and space.
Here I have to submit that further comparison with es "it", etc, will be out of scope.
For the sake of the argument, it's enough to assume that German io vel sim. and Italian cosa were simply run together in a zone of contact. Understanding of an indefinite pronoun seems exceedingly likely, across the board, but I have found no direct evidence in the books.
At best, one might note that puns like x-mas, or x-beinig "to toe in, knock knees", could well point to Norse kers "cross" in a pressumably older sense of *kr-kers "bend, crooked" etc. (cf. Pokorny: *sker-). Whereas score, which belongs to the same root, does not only suggest a sense of tally marks (cf. Roman Numeral X) or hashed tables (cf. hatchet) but in particular the underscore as place holder. In maths, the unknown quantity is very often the zero-crossing (or root of a polynom) or the angle ∠. (NB: Iota is a biblical metaphor for a small quantity, which seems to refer to a character, too).
Which is to say, to falsify the above in toto, another question has to be asked.
- if [ɛks] is a spoken name for the symbol 〈x〉, where does it come from (the name-meaning pair)?
eks goes to Etruscan, presumably. The letter has no clear predecessor in earlier Alphabets. The rune Gebo 〈ᚷ〉 almost seems to agree with the sound value. Elhaz "elk" 〈ᛉ〉 matches each < OE ælc so much better and 〈ᛉ〉 is in fact transliterated variously as [ks] but also [z] [ɻ], [y] depending on context (NB: possibly [s], if you fancy Phrygian, cf. Bartomeu Obrador Cursach, Lexicon of the Phrygian Inscriptions, dissertation, Barcelona, 2018).
So, to return to your initial question:
My question is, is it correct to view the writing 'x' as the written form of the spoken sound ɛks, which (ɛks) in turn is a spoken name for the symbol x?
No, not really, that seems mechanistic. My take does not improve on it much, if instead you were looking for a theoretic methodical treatment. It is notable that the conceptualization of those distinctions is difficult and therefore often simplified before becoming formalized. Beginning perhaps with Saussure's parole, the pair of form and content is a unity which cannot be separated without rendering the symbol (here X) meaningless. However, linguistics gives little attention to the graphematic toolbox. See the search results, especially Why does linguistics focus on spoken languages rather than written ones?.