One of the interesting things about Greek is that it often has fewer specific words than English - or at least doesn't have equivalents for many of the precise and specific terms we have in English. So some of the subtle distinctions we might draw by using different words cannot be communicated directly the same way in Greek as it's just the same one word for what we would consider to be distinct concepts in English.
For instance, to take a less abstract example, Greek uses the same word for "arm" and "hand" (or "foot" and "leg"). You take the specific meaning intended from the context rather than the word itself. It's curious as a native English speaker as I often feel like I'm being too vague when talking in Greek because I want more specific and precise words for certain things. However I think it's quite useful to bear in mind as a characteristic when reading a translation of a Greek text.
I just found this written by Wilson on her translation of this epithet, which is probably more compelling than my take: https://open.substack.com/pub/emily613/p/on-complicated
Also this:
πολύ-τροπος , ον, (τρέπω)
A.much-turned, i.e. much-travelled, much-wandering, epith. of Odysseus, Od.1.1, 10.330.
II. turning many ways: metaph., shifty, versatile, wily, of Hermes, h.Merc.13,439; “τοῖς ἀσθενέσι καὶ π. θηρίοις” Pl.Plt.291b; and in this sense Plato took the word as applied to Odysseus, Hp.Mi.364e (Sup.), al.; τὸ π. τῆς γνώμης their versatility of mind, Th.3.83; τὸ π., of Alcibiades, Plu.Alc. 24.
- fickle, “ὅμιλος” Ps.-Phoc.95.
- of diseases, changeful, complicated, Plu.Num.22; also “πόλεμος τοῖς πάθεσι ποικίλος καὶ ταῖς τύχαις πολυτροπώτατος” Id.Mar.33; “στρατεία” Eun.Hist. p.223D.
III. various, manifold, “ξυμφοραί” Th.2.44; ἐπιθυμίαι, ἐθισμοὶ τῶν λέξεων, Epicur.Fr.471, Nat.28.1 (p.7V.); “κακά” Ph.2.567; “ἔθνη” Plu.Marc.12; “τύχαι” Id.Alc.2; “ὄργια” Lyr.Alex.Adesp.36.3; “τὸ π.” Phld.Sign.26. Adv. “-πως” in many manners, Meno Iatr.20.31, Ph.2.512, Ep.Hebr.1.1, Iamb.Comm.Math.12: Comp., “-ωτέρως καὶ ποικιλωτέρως” Epicur.Nat.5 G.
Henry George Liddell. Robert Scott. A Greek-English Lexicon. revised and augmented throughout by. Sir Henry Stuart Jones. with the assistance of. Roderick McKenzie. Oxford. Clarendon Press. 1940.
https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0057:entry=polu/tropos