Please advise what is the disorder called when you're born with your brain outside your head?

Not aware of one. There is an abnormality called anencephaly, where the top of the head is not closed, and most of the brain does not form. The face appears normal to some point above the upper eye brows, over to above the ears and backward. The top of the head may have a thin film covering where the skull would be, but it is usually gone or torn during delivery.