Not in bad faith, it's not easy to quickly find something that would fit exactly the case with "ERE" (at least for me). West Frankia seemed the closest match since many years before the 1337 start date "Frankia" was divided into "West" and "East" one (and I remember learning about it in school, so someone is using those names today). Those names lost the meaning in 1337, just as "ERE" lost its meaning after "WRE" fell. What was (sometimes?) called "Eastern Roman" ("Imperium Romanum pars Orientalis"?) simply became "Roman". You can't have "east" without the "west" and vice versa.
"Really matter"? No. It's not something I would die for (though I'm still fine with being cut to pieces by some forum members). But I believe that from these three choices:
1. Byzantine
2. Eastern Roman
3. Roman
third one is the best and most historical, so replacing first one with second one is an upgrade, but suboptimal.
Oh but there is, I know it very well as non native English speaker who makes a lot of mistakes. Languages have rules. Some rules you can break and people will understand you, but they will notice that "no one speaks like that" ("I is of thankings"). And some rules, when broken, make it very difficult to understand the meaning - as the infamous "Chinese bootleg Star Wars" humorously prove.
It's valid, but that doesn't mean we can't pursue the better alternative than an ahistorical one made long after Roman Empire ceased to exist.
Oh, I have another one, maybe better this time. Why EUIV uses "PLC" instead of "Poland"? That's how many modern people call "PLC" and those who know history know what they mean when they refer to PLC of XVII century as "Poland". So, according to your definition ("I know what they meant, you know, everyone else know, so it's valid") it would be valid. But would it be historical? Proper? Would people defend it and say "there's no way to please them, everyone knows what Poland means, so what's the point in naming it PLC?"?
I believe PLC is a better alternative than "Poland" even though modern people use both terms.
Just as I believe "Roman Empire" is a better alternative than "Eastern Roman Empire" even though modern people use both terms.
There are many things I like about games like this one. The main one is the ability to create alternative history. But almost equally important is the knowledge I gain just by playing. There's plenty of states and other things like situation in particular region that I learned about from this game. And it's awesome, because history lessons at school couldn't focus on everything and not everything is interesting enough to me to just pick a book and read about it. But here - I can learn things while playing. I know, I know - "it's not game's job to teach history". But it would be awesome if it did and stick to history as much as possible instead of "I must apologize for Wimp Lo. He is an idiot. We purposely trained him wrong, as a joke".
That's the reason. I like Romans, I'm probably a "byzaboo" (though I often exaggerate a bit as a joke), but this preference isn't limited to Rome only. I would love to see all tags named as they were historically at that time, because that would help me with immersion (and I care a lot about that) and I would learn cool stuff. It's okay to know "Turkey". It's better to know it as "Ottoman Empire", but it's even cooler to know it as "Devlet-i ʿAlīye-yi ʿOsmānīye" or "Sublime Ottoman State".