Solinus spoke of Βριτόμαρτις Britómartis as a native Cretan name for Artemis, the Greek goddess of moon and hunt, which he claimed had underlyingly meant virgo dulcis 'sweet maiden' and Hesychius doubly equates his Cretan gloss βριτύ with Greek γλυκύ 'sweet'.
Apparently though, from what I've dug up so far, this is all that's ever written on the subject of the etymology of her name, an important question that's tossed aside for airy interpretations of local mythology to fill up the latest tome weighed by the pound. Out of desperate curiosity, I consulted Wikipedia to see if any of those busy bees had found just a smidge more than the status quo but predictably the groupThink swarm proved once again worthless. There's far more to the origins of this name but the following exploration is curiously absent in any book I'm aware of on the subject despite being, I believe, highly illuminating.
The first element, brito-, may remind us of the Greek example of ἄμβροτος 'immortal' from Proto-Indo-European *n̥-mr̥tós 'non-dying' showing how easy it is for /m/ to strengthen to /b/ before another resonant. In light of Hittite militu- '(honey)sweet', a characteristically Indo-European u-stem adjective derived from milit- 'honey', there should be no doubt where the first element comes from. The second part of the compound, -marti-, is contrastingly sourceable to Assyrian mārtu 'daughter, girl', a purely Semitic feminine form of māru 'son, boy'. These linguistic connections complement the already well-known Anatolian and Near-Eastern influences on Crete.
 Solinus, Polyhistor, 11.8.
 Puhvel, Hittite Etymological Dictionary, version 6 (2004), p.155: miliddu-, maliddu 'honeyed, (honey)sweet'.
Paleoglot: My sweet honey bee