I know of a case in the UK about forty years ago, where the bullet never penetrated the skull, it just skimmed across the surface. I think it was a .32, but I’m not completely sure. Either way, this is not the norm.
If the bullet penetrates the skull, there’s going to be brain damage. Not in the “I can’t brain today, I has the dumb,” kind of way, but they’re still going to be a bit messed up.
There was an American series called Touching Evil about ten years ago, where the lead character was a cop who’d been shot in the head and was trying to deal with the resulting brain damage. It was a remake of a British series, I haven’t seen. Unfortunately, the British series is the only one that’s readily available, and I don’t know how well that incarnation handles the character’s psychological issues.
The other thing that comes immediately to mind is, someone can still suffer serious burns from having a gun go off at close range, even if they aren’t actually struck by the bullet. It’s entirely possible the bullet missed your character and they were still deafened in one ear or blinded by the gunshot. (By the way, this CAN actually happen with blanks at close range. So it’s a plausible outcome for someone trying to “scare” your character by mock executing them with a blank. For reference, mock executing someone with a blank can still kill them, because of the burning wadding.)