Deuteronomy 33:2 and Judges 5:4-8 seem to imply Seir was once a Holy Mountain of Yahweh as much as Sinai was.
The Bible mentions the names of the Idols/Abominations of the other people around the Israelites a lot. The Caananites (including the Sidonians/Phoenicians) worshiped Baal and Astarte, the Philistines worshiped Dagon, Moab had Chemosh and Ammon had Moloch/Milcom. None of these were the only gods of those pantheons (the pantheon as a whole overlapped), but they were the most popular and/or the patron deities.
But no such Patron deity of Edom is mentioned. Now I think the Edomites probably came to worship Yahweh in an idolatrous fashion. Not unlike the Northern Kingdom, which besides the brief Baal system under Jezebel was always Yahweh worshiping, it had Kings with Yahweh theophoric names like Jehu and Jehoram.
In I Kings 11 the Edomite wives are implied to be as complicit in leading Solomon into Idolatry as the rest, but their own Idol isn't named. I think the other wives promoted their alternate gods, and the Edomite ones played the role of coaxing him into thinking it need not conflict with being faithful to Yahweh.
Some may say the Hittite Idols weren't named either. The Hitites of The Bible were NOT the Hittites of Anatolia, I know many in Apologetics have come to love that identification, but it doesn't fit. Those Hittites were Indo-European, in my view probably descended from Chittim. Their land wasn't subject to David and Solomon as the Biblical Hittites were. The Biblical Hittites were another Caananite tribe and so probably worshiped the same Idols as the Zidonians. In fact the Hittites are sometimes mentioned in ways that imply thy're geographically closer to Jerusalem then Zidon. Actually reading Genesis 23 and 25 tell us the Hittites/Children of Heth lived in the area of Hebron.
Qos/Kaus is an Edomite god imagined by Scholars only from that name being part of the name of two Edomite Kings known from Assyrian inscriptions. They may have indeed worshiped a god by that name also as they became polytheistic in their Yahweh worship. But it's also possible that name was just a royal family name.
However since I agree with Bill Cooper in After The Flood Appendix 1 that the Idumeans were of Ishmael's son Dumah, not Edomites. And we know they are linked to Qos via names like Costobarus. And Quzzah is evidence of Qos being worshiped by other Arabs. I think maybe these Edomites of Assyrian inscriptions were also the nation of Dumah, who Isaiah 21 does link to Seir about this same time.
So how does this fit in with Edom becoming Rome?
The Edomites who came to Italy (I suspect they came in different waves) eventually intermingled with Indo-Europeans, and more or less adopted their language and religion over time.
But Roman religion as we tend to know it comes from their much later merging it with Greek mythology. The sacking of Rome by Gauls in the 390s BC destroyed a lot of their earliest records. But Plutarch says the second King Numa Pompilius
"forbade the Romans to represent the deity in the form either of man or of beast. Nor was there among them formerly any image or statue of the Divine Being; during the first one hundred and seventy years they built temples, indeed, and other sacred domes, but placed in them no figure of any kind; persuaded that it is impious to represent things Divine by what is perishable, and that we can have no conception of God but by the understanding".And that was kept up for 170 years. Numa was contemporary with Hezekiah, maybe he was inspired to try and bring Rome back to the true worship of the Patriarchs.
The Roman/Latin form of the Indo-European Dyeus Pater (who to the Greeks was Dios/Zeus) was Jupiter, originally Iopater/Iupater/Iupiter. The "Pater" part means father, it's one of the words Latin has in common with Greek. Ju/Jo/Io is the shortening of Jove or Iove. The actual word Dyeus in Latin became not the proper name of a deity but their word for god, Deus. Jove is also one of the Roman deities who's name wasn't derived from Etruscan, the Etruscan Zeus was named Tinia. Roman mythology also had an alternate storm god, Summanus, he did come from the Etruscan pantheon.
Yahweh is never rendered in Greek in New Testament manuscripts or the Septuagint or Josephus or Philo or any other Judaic Greek works for a number of reasons. The Rabbinic Jewish superstition of not pronouncing the name of God due to a flawed understanding of the fourth commandment was already developing. The New Testament goes along with it I believe only because Yeshua/Iesous/Jesus has superseded Yahweh as the personal name of God.
Rendering YHWH in Greek would be difficult due to only one of the letters even having a solid Greek equivalent. But one Greek text does seem to show us how it might have been rendered.
According to Eusebius, Philo of Byblos, a Hellenized Phoenician, claimed his probably made up source Sanchniathon used as a source a book by a Hierombal (possibly a Greek form of Jerubaal, a Hebrew name that appears in The Bible only as an alternate name for Gideon) who he calls a Priest of Ieou. Ieou makes sense to me as a Greek rendering of Yahweh due to it happening to be how Jesus is rendered in Greek only minus the Sigmas. Yeshua spelled in Hebrew without vowels has the same first and third letters as Yahweh.
In Latin manuscripts Ieou becomes Jevo. Jevo can become Jove simply by switching it's vowels around. So maybe it's possible Jove came from a corruption of the name Yahweh?
Now Edom-Rome once again worships the Biblical God but in an Idolatrous Fashion, via Catholicism. Vatican Hill is the new Mount Seir.
Update 1/23/2016: I've changed my mind on the proper pronunciation of YHWH, I now favor Yahuah.