I wonder what would happen if modern day Italians decided to call their country "the Roman Republic", and the ERE was still around.
Or if the WRE and the ERE had split up for good, I'm pretty sure the WRE would have been considered the "original".
The ERE evolved very differently from the classical Roman Republic, and it's highly unlikely that at least some of this wouldn't have been different, if the WRE had remained a part. Still, at the time, the ERE was the closest inheritor.
Apart from this, it's just a label.
Or if the WRE and the ERE had split up for good, I'm pretty sure the WRE would have been considered the "original".
The ERE evolved very differently from the classical Roman Republic, and it's highly unlikely that at least some of this wouldn't have been different, if the WRE had remained a part. Still, at the time, the ERE was the closest inheritor.
Apart from this, it's just a label.