You are called "The Last of the Jedi" because it is BELIEVED that all of the other Jedi have died either physically or mentally. There was only two fates left from the two wars they faced. Either you died in one of the two wars in combat or the events hit you so hard that you turned away from everything the Jedi stood for.
Still, Krea and the Sith Lords believe you to be the last one because they believe that you are the only one left that will do anything to stop them, such as a Jedi would.
The game is confusing at the beginning because the game was basically rushed to be finished. Instead of taking the time to make sure that the game was finished and bug free as possible, they were trying to rush to make a deadline that they ultimately wouldn't have been able to meet.
I'm not going to give away the game or anything, but the confusion is cleared up the first time you board the ebon hawk and have a good talk with Krea.
Hopefully with the new KOTOR game that they'll be making, they will make sure that they give themselves enough time to design the game in a way that's as bug free as possible, and making sure that the story line was better laid out. Most people like KOTOR1'S story line because you get into more details and you end up having more clearity about what's going on and the game itself.