That's a shame. I'd sand the headstock down to remove the paint and if there were still visible gouges, stick on a piece of veneer then paint that black. No need to go overboard, you can probably just put a few coats of paint on, sand that down and buff it up when cured without bothering with clear gloss.
Alternatively, you could try colouring the chips in with a black sharpie or paint, filling the chips with superglue until slightly proud of the headstock then sand the dry superglue back to level then polish it up. But it's probably less overall hassle to add some veneer.