What is the name of the farthest star in our galaxy?
Because of the way we are situated in the Milky Way Galaxy, the furthest point away from us [See related pictorial] is obscured from our view by the Galactic core, and so we have no idea what is out there.
There are stars out there, but for now, we just don't know what they are.
Just about as far as the closest star in the Andromeda Galaxy. The diameter of the Andromeda galaxy is ... well, quite huge, but still relatively small, compared to the distance between us and the Andromeda Galaxy. And I believe this diameter may still be smaller than the uncertainty in the distance estimate!