Twilight Divine Beast epithet? The Ordon, the Twili, the Zonai? I just found your fic a Change in Fate and I am /very/ curious.
This took me a bit to answer because I had to find the text conversation with my friend this came from.
Originally this whole theory started with us talking about phenotypes and genotypes in the Links. This isn't relevant I just find it amusing this was the conversation happening at the time.
At some point in this conversation, my best friend almost randomly asked me "Wait are the zonai descendants of Ordon village?"
Firstly, Ordon is in the right place. The Ordona province in Twilight Princess is south of Faron, though by Breath of the Wild that entire area is considered Faron. (I don't know if this was mapmaker making mistakes at one point, or Faron moving in to engulf Ordona. Doesn't really matter either way.) And the Zonai are from Faron, so they're in the right area.
How do the Twili fit in? Well, a lot of people consider the Zonai to be Twili in some way. So, I did some thinking.
Let's assume Twilight and Dusk manage to fix the mirror, and they find a way to let any Twili return to Hyrule and live there without the need of the Twilight covering the area. This isn't a leap, all Zonai = Twili theories require this assumption.
So, with these assumptions, we can naturally assume that at some point after this Midna will have to work with Dusk to set up a small Twili colony in Hyrule. And of all the places to put this colony, I think it'd make the most sense to put it in Ordona. There are only two hylians to ever end up close to a Twili, and that's Dusk and Twilight in regards to their relationship with Midna. Meaning it'd make sense to put the colony next to the home of one of these hylians, since there's a preexisting relationship to help ease the transition. And, putting it near the capitol doesn't make as much sense. Dusk is too busy being queen to act as an ambassador of sorts in the day to day, and I don't think the people of Castle Town would be eager to welcome the Twili. Ordon village, however, was never actually attacked by Twilit monsters, since we save Ordona before her light is stolen, so there's less bad blood there to start with, and Twilight's job means he can spend more time at home building a closer relationship between the cultures.
Furthermore, the Zonai have two notable aspects about their culture revealed in BotW: they were powerful magic users, and they were considered barbarians.
The Twili have a natural talent for powerful magic, but unless they've been turned into monsters they don't seem to be fond of physical fighting. Conversely, the Ordonians are not magically inclined at all, but they are physical fighters, with both swordsman and wrestlers found among them. (Some of them, like Twilight, are both!)
I like to think the Zonai were likely the result of the Twili and Ordonians merging their cultures and intermarrying. It's not as out there as any other theory, anyways.
So, what does this have to do with Twilight's 'Divine Beast' epithet? Well, that's pretty simple.
At the end of Twilight Princess, only a small group of people know Twilight as a Divine Beast. Midna and Twilight, of course, as well as the Sages, since they were there when Midna came clean about everything. I don't know if even Dusk knows about this title. And yet, by BotW it's well known enough to have powerful animal-shaped machines named after him. So, what happened?
I think Midna would have wanted to honour the hylians who helped her save her people, even after everything they lived through. And besides, Midna said her people had a prophecy about a Divine Beast coming to save them. It'd make sense she'd let people know she fought alongside this Divine Beast, and talk about who he is. So, when they made the jump to the colony, most Twili would know the Divine Beast was a Light Dweller and Hero.
This of course would mean the epithet was used more often, and would have existed when the merge into one culture happened. With the Zonai calling the Hero of Twilight the Divine Beast, it would make sense that by the time the sheikah made the Divine Beast machines the title was well known enough that Twilight could be the namesake of the giant mech animals.
TL;DR: I think the Zonai were the result of a culture merge between the Twili and the Ordonians, and that's why enough people knew of Twilight's Divine Beast epithet for the Divine Beasts to be named for him.