"Their names are both Trevor" would sound the most unambiguous to me.

I would just say "They're both named Trevor."

Trevor're their names.

The trevors are named trevor.

They’re named Trevor.

Them be Trevors

Both don't sound right as they are ambiguous. "Their name is Trevor," sounds like it is talking about a single person. "Their names are Trevor" feels incomplete. "They are both named Trevor" or "Their names are Trevor and Trevor" solves that ambiguity.

"They're both named Trevor."

We are all Trevor

“Their names are Trevor.”

Their names are Roberts Paulsons

Both their names are Trevor

As somebody who worked in a place with 5 Dougs, I would say their names are Doug. Beyond that, they get descriptors. Angry Doug, Cool Doug, Vac-Former Doug, Smiley Doug, and Doug 2.

My interpretation: “their name is Trevor” is grammatically correct, but semantically means their collective name is Trevor, not that they’re both called Trevor.

“Their names are Trevor” is incomplete because the subject implies a plural while the object is singular. This could work if you were to list multiple names: “their names are Trevor and Trevor.”

You could use some Irish English, then you could be saying "Themmuns are called Trevor" that way there's zero ambiguity

“Their names are Trevor and Also-Trevor”.

I present: THE TREVORS

If you are referring to only one of the two, it is "their name is Trevor". If you are introducing both of them at once (possible, but less likely), you would say "(both of) their names are Trevor". Sometimes people also pluralise the name, e.g. "I'm friends with five Alices" or "I know two Bobs at work"

The sentence that comes to mind is “both of their names are Trevor.”

For your question, this conveniently reduces to “their names are Trevor.”

So there’s your answer.

If the pair together have a name, the pair's name "is Trevor" but if they're each individually named Trevor, their names "are Trevor."

"These are the trevors"

"These are Trevors one and two"

I used to know 3 guys named Cody. Eventually their names evolved into Co-one, Co-two, and Co-three any time we were referring to them outside of individual.

The name has no plural here because it is the same: Their name is Trevor.

Add one vote for "are".

And Trevor is his name-o

Both correct, it depends whether you are saying,1 "They both have names and their names are Trevor" or "They both have the same name and that name is Trevor".

So the real question is are you talking about their shared name or both of their names separately?

"A Trevor trove of flavour lies within".

"Who's Trevor?".

As others have said, neither is good English.

That being said, you're referring to two people, so are is the less incorrect version in that specific example. I'm way too long out of grammar classes to remember the right terminology for the underlying "rule", but it comes down to what the target is.

They are Trevor is a more compact version of they are both Trevor, which is again the short version of they are both named Trevor.

So, it comes down to sticking as close to that as possible. Their names are Trevor, because there's a single name, but plural people. Both people possess the name Trevor. Trevor is their name.

That's usually the way to figure out the least wrong/closest correct way to say something. You shift the wording until you get something that scans right to your brain, and most of the time you're as close as you'll get with conjugation of "to be"

And it's weird as fuck that "to be" is so transformed. Is, am, was, were, are, been, being, and even weird shit like "be going to" and "going to be". Like, wtf English? Why you gotta bring extra words to the party like that? You really need a second verb to conjugate a verb?

There's some weird etymology shit going on there somewhere between old English and it's roots. Hell, the fact that "to be" is even necessary is a little weird. Like "ser" in Spanish. It means the same thing, but lacks the weirdness of to as a butt buddy. Mind you, that shit conjugates weird too! Yo soy muy mindfucked by Spanish too, and I bet tu eres mindfucked tambien. Like, really, go look up the conjugation of ser. It isn't as wonky as to be, but it's getting there, especially in the imperfect tenses.

I don't even speak Spanish worth a damn, much less any other languages, but I bet every language has some fuckery like that in it. I'm just really gobsmacked at the verbal gymnastics of the two I'm familiar with. But the English version of the underlying idea is just an extra layer of tomfoolery.