If you can't even answer something like this, then it proves your lore department is non-existent.
EDIT: I have my doubts that they're just called "Demacia" and "Noxus". That sounds kinda lazy and unrealistic.
Demacia and Noxus were often referred to as city states. So its likely that Demacia and Noxus are the capitals and they reign over the surrounding territory.
Yup, Demacia and Noxus are city-states rather than enormous nations. Thus, Demacia is the capitol of Demacia and Noxus is the capitol of Noxus. And before anyone says it doesn't make sense, remember that city-states were incredibly common for most of human civilization (Nationhood is relatively recent) and a few city-states still exist, the most notable being Singapore, Monaco, and Vatican City.
The cities we all referred previously to as Demacia and Noxus in the old lore are the Capital cities of The Kingdom of Demacia and The Empire of Noxus.
I get a 
gold ascension pendant for my work, thank you.
Well they are city-states so the capitals will probably share the same name as the country. Sparta and Athens were also city-states with their territories being known as Spartan or Athenian.
Geese, I say it first but I get downvoted. Sharjo says it and gets upvotes, seems like I have haters now.
Demacia nad Noxus... IZ.
Where is my price 
kappa
They started as simply the city states Demacia and Noxus, but have each since then grown to full blown empires.
It works in the same way that Ancient Babylon used to be a city state, and then turned into an empire. The empire was still called Babylon, just like the original city state.
