According to PGE1, Argonia is named after "some ancient battlefield", and PGE3 mentones Battle of Argonia, too.
The bit in the PGE1 refers to "some ancient battlefield where many of their ancestors fell", "their" referring to the Elves, but this is interpreted as crazy Septim propaganda by the (presumably) Altmeri commentator. The bit in the PGE3 is referring to the battle where Reman's army finished off the Argonian one.
I doubt an Imperial propagandist would want to attribute the site of one of Reman's conquests as an Elven battlefield, so these are two different battles, assuming the one in PGE1 even happened. Argonia/Black Marsh doesn't even appear in historical records prior to the Battle of Argonia, and I doubt Reman's army came up with the name on the spot.