Many are Greek, though they’re old and obscure enough to be headscratchers. If they aren’t Greek, they certainly aren’t going to be Hebrew or Persian (Greeks were in Greece a long time before they were anywhere near either); the origins of non-Greek names are more readily sought in old Anatolian and Middle Eastern civilisations, like Ugaritic or Lycian.
Zeus is the Greek continuation of *Di̯ēus, the name of the Proto-Indo-European god of the daytime sky, also called *Dyeus ph2tēr (“Sky Father”). The god is known under this name in the Rigveda (Vedic Sanskrit Dyaus/Dyaus Pita), Latin (compare Jupiter, from Iuppiter, deriving from the Proto-Indo-European vocative *dyeu-ph2tēr), deriving from the root *dyeu- (“to shine”, and in its many derivatives, “sky, heaven, god”). Zeus is the only deity in the Olympic pantheon whose name has such a transparent Indo-European etymology.
That wikipedia artcle quotes from Burkert’s Greek Religion, so let’s see what etymologies he mentions as likeliest:
- Hera: hōra “timely”? “ready to get married”?
- Poseidon: Lord of… the Earth? of the Waterways? Source of Waters?
- Athena: Athens may have come first, -ene is a location suffix.
- Apollo: God of the Apellai initiation ritual
- Artemis: probably from Asia Minor; proposals include “healthy”, “butcher”, and “Bear Goddess”
- Ares: Chaos of War.
- Hermes: from herma, a cairn of stones (with phallic cultic connotations)
- Demeter: not in love with the traditional etymology “Earth Mother”, but somehow it connects to cereals.
- Aphrodite: Proceeding from the foam? Adaptation of Phoenecian Ashtoreth? Phoenecian “dove” or “fertile”?
- Dionysius: Zeus’ Something, but Zeus’ Son is guesswork, and the second bit may be non-Hellenic. The other names are certainly non-Hellenic: Bacchus is Lydian, Thyrsus Ugaritic.
- Hephaestus: Not Greek, and there has been speculation of Etruscan (via Lemnos) and Lycian origins.