We don't know how far Mede's dynasty goes, so I say NAY to "medes." Besides, if you want people to legitimately support you, you should maintain a popular currency named after a popular and successful dynasty. There's no reason to change something that's been called "septims" for at least 450 years. The Empire in Skyrim probably claims direct lineage from the Septim dynasty, anyway.
The Rebels probably use it for the same reason (i.e., claimed lineage from the Septim dynasty).
Septims are named for Tiber Septim, and have his bust upon it. Tiber Septim is now Talos and therefor the Septims feature Talos, and Mede has thus banned the worship of Talos (failure to abide by that law = death, or so I've heard). The empire is crumbling, the Septim Dynasty is completely over. The a new dynasty has begun. It would make sense to have the empire use different currency.
Given that Mede's empire and the rebel Stormcloaks are at odds, it would make sense for them to utilize different currency. For example, during the American Civil war, the Confeterates (rebel) did not utilize the currency of the Union (empire). If anything, the Rebels would utilize Septims, and the Empire would use Medes (or anything other than Septims)...
But it has been 200 years since the Septim Dynasty has ended... One would think that
something would change in regards to currency, especially due to the conflicts in the other provinces....