In Japan, they had names for their seasons, yes. Elsewhere, most places just dropped the names and called 1, 2, 3, and 4. In truth, I wouldn't have even known about the names if I hadn't been looking up Digimon on the net.
Season 3....bugged me. That's all I can say. I never felt like we ever got a deep enough, or long enough plot line. I think moving the main action to the Real World was a mistake. I much preferred the seasons where they fought in Digiworld, with maybe a LITTLE bit of fighting in the Real World.