Ancient Greeks (Ionians), among other Gods, worshipped Iaon (God of the rain?-compare deluge).
Source? I have never heard of a Greek god named "Iaon". I think you mean Ion (Iων), who was the eponymous ancestor of the Ionians; cf. Javan (Yawan), the son of Japheth in the Table of Nations and Javan as a name for "Greece" in the OT. Japheth is also thought to derive from the Titan named Iapetus (Iαπετυς) from Greek mythology, so the Hebrew representation of the origin of the Greeks probably has a Greek source, perhaps via the Sea Peoples who settled on the Levantine coast (especially the Philistines). Also Ion wasn't a rain god, nor had any connection with the Deucalion deluge traditions iirc (which are thought to have been cross-fertilized from the Mesopotamian flood myths via Asia Minor).
Iaon=Ionian. It is clear that Ionians got their name from their God Iaon.
Umm, its probably the reserve. Eponyms derived from the tribal name...just as in the sons of Jacob whose names are derived from the actual tribes. We know that the tribal names have priority because they have geographical meaning....Benjamin being located in the south in Palestine, Naphtali being the highlands, Ephraim being the fertile farmlands, etc.
Iaon = YHWH.
Why? What relation do the names have beyond some kind of superficial resemblence? This is like saying Lazarus is derived from El-Osiris. There is no basis for equating the West Semitic cult of Yahweh with an obscure eponymous ancestor of the Ionians (whom I'm not sure if there was even a cult of, as opposed to being a character from mythology).
Another Greek word that bears the name of YHWH is iahi (=battle cry).
So which is it? This is a totally different supposed source. And where is it attested that this was a war cry in Greek?
In fact, YHWH (in the form YHW) was first attested by the Egyptians in the 18th Dynasty as a PN associated with the Edomites, long before the incursion of Greek-speaking Sea Peoples into the Levant (later on in the 19th Dynasty).
So they were shouting/calling the name of Yah, their God, and threw themselves in the battle.
There is not a single scholar on the ANE that has suggested that.
Of course Baal along with human sacrifices to him is not absent from ancient Greece either.
Which Baal? "Baal" is simply the word for "lord" and was applied to many gods. Most of the references to Baal in the OT were to Baal-Hadad, the storm/rain god, who was syncretized to Yahweh. There was another Baal introduced into the Northern Kingdom from Phoenicia who was probably Melqart, and this god was possibly associated with human sacrifice. But the god in the OT associated with this was Molech, and this probably pertains to the Milku from Ugarit who was a sort of chthonic deity....and the connection between the two is more ambiguous. Also El was associated with human sacrifice among the later Punic Phoenicians, under the name Baal-Hammon (his identity with El is confirmed by classical writers who referred to him as Kronos or Saturn).
Even today the name of a town/suburb near Athens bears his name: Pallini.
LOL. Are you seriously claiming this??
From ancient Greek texts we find that the name of the suburb was then Ballini which is a clear derivative of the plural of Baal: Baalim.
"Clearly"?? What? There is nothing clear about that at all. Just an instance of inexact phonetic similarity without any supporting evidence of a historical connection, or even sources to substantiate the claim.
BTW the name was spelled Παλληνη in Greek, so your vowels appear to be wrong, and what is your source about the initial "p" originally being "b"? If one wants to find a mythological origin of the name, one could find no better phonetic parallel than Παλληνη, one of the Alkyonides. No similarily whatsoever to Baal; for starters Παλληνη was female, and the Alkyondies had been transformed into birds.