Standard etymological reference works record both Skylla and Kharybdis as of unknown origin. Scylla's traditional folk association with skylax ("young dog") and skyllein ("to tear") fits her description but is not treated as a confirmed derivation, and no comparable folk etymology exists for Charybdis at all.
What would resolve this A securely attested Pre-Greek or other substrate source for either name, or a phonologically sound Indo-European derivation succeeding where the traditional dog-and-tearing folk etymology for Scylla has not been confirmed as more than an apt later association.
OpenHistorical and comparative Indo-European linguistics, Pre-Greek substrate studiesDouglas Harper, Online Etymology Dictionary