The region that we know today was always addressed as Karnata/ Kuntala from the beginning of time. Karnataka/ Karnata both mean the same. The Chalukya armies were called as Karnatakabala and not as Mysurubala. The Vijayanagara Empire’s actual name was Karnataka Empire or Karnata Empire. The organization that led the movement for the Unification of all Kannada speaking areas was called as Karnataka VidyaVardhaka Sangha and the movement itself was called as Karnataka Ekikarana movement.
Karnataka name has always been constant and only the size has varied. Under the Chalukyas and the Rashtrakutas, Karnataka meant the entire stretch from the Godavari in the North to the Kaveri in the South. Under the Vijayanagara Empire, it covered most of South India. It was after the fall of the Vijayanagara Empire that the United Karnataka was split into parts which remained the case till 1956.
In 1947-48, Kannada speaking areas were broadly divided into 20 states. Out of these 20 states, Mysore had the largest number of Kannadigas and in 1956; some of these 20 states were integrated with the existing state of Mysore to form one united state where Kannadigas were in majority. Hence, the name Mysore remained. However, the renaming should ideally have taken place in 1956 itself, because the political movement in Karnataka says Mysore was just one part of Karnataka and Karnataka actually extended from Godavari to Kaveri at once upon a time. Mysore state did not do justice to the name Karnataka and it was rightly renamed as Karnataka in 1973.