Dovahkiin is not a name, it's a title.
Dovah = Dragon, kiin = Child / Born. Dovahkiin = Dragonborn
Tiber Septim was also Dovahkiin, as was Martin Septim before he... well, I'm not gonna spoil it for you. As for the Dragon language that you learn in the form of shouts, it's called "dovahzaan" - the Dragon Tongue.