A person who makes hats is called a milliner or a hatter. Milliners are specifically those who are adept at the process of making, designing and selling women's hats, while hatters are more likely to focus on hats for men.
The terms "milliner" and "hatter" are often used interchangeably. The term "milliner" originated in the 16th century from the name "Milan," a city in Italy known then for the lavish items sold there. A "Milaner" at the time was a native vendor of these goods, so the term "milliner" evolved for the person who made and sold fancy women's hats.