Christianity didn't actually get the name until the Apostles were doing stuff in Antioch... Dunno what year, but it was well after Jesus' crucifixion. Scripturally, it says in Acts that early Christians were called "Followers of The Way." Apparently, another early name (according to Wikipedia anyway) was "Nazarenes," which was a reference to Jesus' hometown of Nazareth.
Very good question by the way... I never really dug into where my religion got it's name before.