either you UVmap only the half of it - but then you would have to delete the other one an duplicate the other half, or you map the whole object.

thing is, every part you don´t map will I think be kind of automapped when created. and every vertex you move afterwards will also change its position in the UVset. but that may be b******t as well what I say.

in every case I´d suggest to map every part wich is used in your scene.