Hesiod, Theogony 154-206: Kronos severs Ouranos' genitals with the adamant sickle, casts them into the sea, foam gathers around the flesh, and from the foam a maiden grows, carried first to Cythera, then to Cyprus, called Aphrodite because she was born in aphros, foam. Homer tells it flatly otherwise: Iliad 5.370 has Aphrodite, wounded at Troy, fleeing to her mother Dione, wife of Zeus, which makes her a thoroughly ordinary Olympian daughter. Plato noticed the contradiction and resolved it by splitting her in two: in the Symposium, Pausanias distinguishes Aphrodite Ourania, born of no mother, from Aphrodite Pandemos, daughter of Zeus and Dione, one for higher love, one for everyone.
Herodotus 1.105 states it as a matter of inquiry: the temple of Heavenly Aphrodite at Ascalon in Syria is the most ancient of all her temples, the Cyprians themselves say their temple was founded from Ascalon, and the Phoenicians founded the one at Cythera. Pausanias 1.14.7 pushes the chain further: the Assyrians were the first to worship the Heavenly one, then the Paphians of Cyprus, then the Phoenicians of Ascalon, then the people of Cythera. The Greeks themselves told the story as an import route, Assyria to Syria to Cyprus to the Aegean, matching Ishtar to Astarte to Aphrodite.
Aphrodite's name appears nowhere in the Linear B tablets, the Mycenaean Greeks' own records, though Zeus, Hera, Ares and Dionysus are all there. Walter Burkert's verdict stands: her origin remains as obscure as her name. The aphros, foam, derivation reads as folk etymology, and candidates for the real root keep surfacing in Semitic, from Astarte to phrases meaning she-of-the-villages. The 2014 volume Transformation of a Goddess: Ishtar-Astarte-Aphrodite tracks the transmission attribute by attribute: the dove, the morning star, the war-lust, the sacred marriage.
Her name will not parse in Greek, she is missing from the oldest Greek writing, and her own priesthood traced her cult to Syria. At what point does an imported goddess stop being Greek?