The potential and density wake behind a finite-sized object in a magnetized collisionless plasma flow is studied with self-consistent numerical simulations. With increasing magnetization of the plasma, the standard picture of ion focusing in the wake for plasmas with large electron to ion temperature ratios becomes invalid. A strong magnetic field parallel to the flow direction leads to a chain of ion depletions in the wake and enhanced ion density at their envelopes. This is due to a novel mechanism of a dynamic ion shadow, which is not the geometrical shadow of the finite-sized object. It corresponds to a change in topology of the wake potential. Complex ion trajectories resulting from electrostatic collisions with the object can lead to significant variations in electrical charging of other objects in the wake.