1. Why would it be lost? The Hero of Morrowind is named Nerevarine even though you get to name him and change his appearance.
Actually, he/she was always known and referred to as 'THE' Nerevarine. ie: 'Nerevar reborn'. It was a title, not a name.
2. Why would you be the last Dragonborn? You're not the last.
Hmmmm...so sure are you? It's apparently been centuries since the previous Dragonborn, who's to say when the next one might arise? A hundred years later? A thousand?