Like many ancient divine names, the etymology of Artemis is unclear (whether it is proto-Greek or non-Greek, etc.). When it comes to etymology in general, I have a fondness for ancient folk etymologies because, even if they make dubious claims, they do tell us something about what the Greeks thought of the deity and how they were approaching their own language. Wikipedia, as one might expect, cites many of the different etymologies for Artemis, but skimps on some of the depth and play available in folk etymology.
The most illustrative example is from Plato (Cratylus 406b) where Socrates proposes multiple spurious origins for the name but then concludes they might all work in concert.
“Artemis seems to be named due to her safe/healthy (artemés) and orderly character, and due to her love of maidenhood. Perhaps, instead, the one who named her named her because she is knowledgeable about virtue ([aretê + manthanô “to learn, know”?]) or, also possibly, because she hates the plowing of a man into a women ([aroton +misê, “to hate”]). Or, the man who gave this name to the goddess named her for all of these reasons.”
“῎Αρτεμις” δὲ <διὰ> τὸ ἀρτεμὲς φαίνεται καὶ τὸ κόσμιον, διὰ τὴν τῆς παρθενίας ἐπιθυμίαν• ἴσως δὲ ἀρετῆς ἵστορα τὴν θεὸν ἐκάλεσεν ὁ καλέσας, τάχα δ’ ἂν καὶ ὡς τὸν ἄροτον μισησάσης τὸν ἀνδρὸς ἐν γυναικί• ἢ διὰ τούτων τι ἢ διὰ πάντα ταῦτα τὸ ὄνομα τοῦτο ὁ τιθέμενος ἔθετο τῇ θεῷ.
I like this passage because it indicates—even if indirectly—the distance between what modern historical linguists do in isolating viable etymologies and how origins of words are engaged with culture and narrative in living traditions. Plato’s characters take what they know about Artemis (she protects virgins, kills some people in horrendous fashion etc.) and what they think they know about language to make reasonable (if historical impossible) proposals. And, more importantly, Socrates, here at least, is reluctant to be reductive: words can mean multiple things at the same time and in this may share their semantic origins with non-cognate roots.
The Doric spelling of the goddess’ name was ῎Αρταμις (Artamis) which is part of what likely led the LSJ to list ἄρταμος (artamos, “butcher”) as a more likely etymological connection than Plato’s indicated ἀρτεμής (artamês, “safe”). But, let’s be honest, everyone likes to argue with Plato (Aristotle especially); and we know that the LSJ is not a result of perfect judgment and absolute science.