Can those limited to the left side of their brains only describe the left half of one's face?
In the diagram below you can see that the left side of each retina (which, due to inversion by optics of the eye, receives the right side of the field of view) is connected to the left hemisphere of the brain. However you would think that a person with right hemisphere damage could just direct their gaze to bring both sides of the subjects face into view on the left side of their retina.
However the problem is real. See Hemianopsia,
Hemispatial Neglect and Fresnel prisms--their value in the rehabilitation of homonymous hemianopsias
a stroke affecting the right parietal lobe of the brain can lead to neglect for the left side of the visual field, causing a patient with neglect to behave as if the left side of sensory space is nonexistent (although they can still turn left). In an extreme case, a patient with neglect might fail to eat the food on the left half of their plate,
Eye movements during visual search in an individual with left-sided neglect attempting to find letter Ts among Ls. Red dots show fixations and yellow lines depict saccadic eye movements from one fixation to another.
This is a partial answer, I don't know any sources that answer whether damage to one occipital lobe invariably leads to hemispatial neglect.