i think by “pivot point” you mean the center of the object which is marked by a small dot.
you can change it by entering edit mode, and moving your mesh the way you want it to be according to the “pivot point”. try pressing TAB and rotating it to the desired fit.
or you could select the vertex you want to be the center, snap the cursor to it (shift-s), go to object mode, and in the mesh-buttons(F9) press “center cursor”