The problem I have with the human invention idea is it doesn't seem like something the Federation would do for official naming.
Except the Federation didn't exist yet during the Earth-Romulan War, and the concept of the Federation hadn't been invented yet when "Balance of Terror" was written. The episode was written with the assumption of an Earth-centric interstellar civilization that had warred with the Romulans a century ago while having virtually no direct contact with them due to the primitiveness of the ships. They didn't know what they looked like, so it's a cinch that they didn't know what they called themselves. They must have gained enough mutual translation to negotiate the treaty eventually, but by that time, the name humans coined for the faceless enemy would presumably have caught on.
It just doesn't fit they would keep a human convention of just making up whatever name they (or the universal translator) picks. Or the Vulcans themselves would be down for being referred to by an "imprecise" designation picked by humans as a reference to our own mythology.
To a modern observer, perhaps not. But the writers in the 1960s wouldn't necessarily have been sensitive to such things.
Also, technically, the visual in "Balance of Terror" doesn't use Remus. It's Romulus and Romii.
Which, on the scale of the map, are obviously two separate star systems, not a pair of twin planets in a single star system. "Romulus" on the map is presumably the star system that contains the twin planets Romulus and Remus, as
Nemesis eventually confirmed. The circle around the "Romulus" star presumably means it's the capital, while Romii is a neighboring system.
Besides, as I mentioned, there are some differences in detail between what the map shows and what the scripted lines say. No doubt the map was made by someone in the art department, maybe Matt Jefferies, and doesn't necessarily match the assumptions of the scriptwriters. Schneider wrote "Romulus and Remus," so of course he intended to reference the mythological twins. "Romii" is just a bit of gibberish the map artist made up.
It's not real, life it's fiction.
It's fiction whose express intention was to be more grounded and realistic than other contemporary science fiction television. Roddenberry was one of the first SFTV creators to consult with scientists, engineers, and think tanks to try to build as plausible a future as he could.
Romulan wasn't a word before Star Trek came along. It's made up,
It is, self-evidently, derived from the name Romulus, one of the mythological founders of Ancient Rome along with his twin brother Remus, and from the demonym "Roman" (Anglicization of
Rōmānus) for an inhabitant of Rome. If Romulus had been used as a place name in Ancient Latin, then the demonym for it could, in fact, have been
Rōmulānus, which would be Anglicized as Romulan. So at most it's only
slightly made up, a minor variation on precedents thousands of years old.
There is no need to overthink a "plausible" reason because it ticks a certain itch in your brain.
It's bizarre that you consider it "overthinking" when it's the most natural and self-evident interpretation. I'm just astonished that I've had to go to so much effort to explain what I would've thought was obvious.