How would one say the name of each individual gate from the Gates of Ivory and Horn in ancient Greek and Latin? According to the Odyssey, they are located in the underworld near the Asphodel fields. I have found that (ἐλέφας) is ivory, and (κέρας) is horn. Pylai means gates (plural) as far as I can tell. So, what would each individual gate be called? I asked this same question in the Mythology Stack, and got πύλη ἐλέφαντος and πύλη κεράων as the answer in Greek.
As Homer put it:
τὸν δ᾿ αὖτε προσέειπε περίφρων Πηνελόπεια·
Then wise Penelope responded:
"ξεῖν᾿, ἦ τοι μὲν ὄνειροι ἀμήχανοι ἀκριτόμυθοι
"Well, stranger, dreams are strange and perplexing,
γίγνοντ᾿, οὐδέ τι πάντα τελείεται ἀνθρώποισι.
and not all of them come to pass, for humans.
δοιαὶ γάρ τε πύλαι ἀμενηνῶν εἰσὶν ὀνείρων·
For there are two gates of shadowy dreams;
αἱ μὲν γὰρ κεράεσσι τετεύχαται, αἱ δ᾿ ἐλέφαντι·"
one of them is made of horn, and the other of ivory."
He never actually uses the words "gate of horn" and "gate of ivory" specifically: here he has a verb (τετεύχαται, "fashioned from") which takes the material in the dative, and later (after this passage) he just uses nouns "the horn" and "the ivory" with no word for "gate". But the answer you got on Mythology.SE is a reasonable one, using the genitive of material.
For Latin, let's look to Vergil:
Sunt geminae Somni portae, quarum altera fertur
There are twin gates of Sleep, one of which is said to be
cornea, qua veris facilis datur exitus umbris;
horn, through which true shades easily make their exit;
altera candenti perfecta nitens elephanto,
the other shines with the luster of polished ivory,
sed falsa ad caelum mittunt insomnia Manes.
but false dreams are sent to the sky by the Manes.
His ubi tum natum Anchises unaque Sibyllam
With these words Anchises escorts his son and the Sibyl
prosequitur dictis, portaque emittit eburna…
to there, and sends them out through the ivory gate…
These ones we can quote directly. Vergil prefers to use adjectives rather than genitives, it seems: porta cornea and porta eburna.