What's the name for people with black hair?

Although there is some debate over this, the Oxford Dictionary definition of brunette is:

noun: a woman or girl with dark brown hair.

This source also mentions that in the US, an alternate form of the word brunette is brunet. The Merriam-Webster definition of brunet is:

a person having brown or black hair and often a relatively dark complexion —spelled brunet when used of a boy or man and usually brunette when used of a girl or woman

Thus, brunette includes the range of hair colors from brown to black. There is no specific and separate term for someone with black hair. However, people have suggested the term noirette. Note, also, that although the term brunette includes those with black hair, not everyone may agree. Therefore, this is the official term for people with black hair but not necessarily the one used in everyday life.

"Raven haired" is an older term that still seems to be understood by most.

A person who has black hair is generally called "black-haired".

Most people will understand.