Honestly I always assumed drakes were just another name for septims. Like how you can call the American dollar a buck or greenback.
I think it's because on one side of the coin is the symbol of the Empire, a Drake, and on the other side is a portrait of Tiber Septim. It'd be like if we referred to American Quarters as Eagles or Washingtons
Wouldn't surprise me if they were called Medes, but that'd only get confused with the popular Nord beverage
But we don't know many details. Given that it's a civil war, I wouldn't rule out the possibility of two currencies. It happened in Fallout New Vegas, where there were actually many currencies. There were the traditional caps, used among wastelanders, NCR Dollars and Cents to spend with the New California Republic, and Denarii (Silver) and Aurei (Gold) to use with Caesar's Legion. Each Casino had its own currency in chips, but let's not go that far with Skyrim
So in Skyrim, given that, there could be the traditional drakes and some sort of Nord currency as well. It'd make things interesting at least. But I don't think it matters whether or not that happens. The Septim was so widespread that it'd probably still have monetary value. I can only think that the elves would create their own currencies. Probably whatever they used before joining the empire.