Hair trap
A hair trap is a strainer fitted in the drain line under a shampoo bowl that catches hair before it reaches the plumbing. Most are a chamber with a removable screen you open and empty, and they also stop hairpins and other small items.
The Marble Products #1701, sold by Buy-Rite Beauty for $55, has an internal screen and is listed as complying with Uniform Plumbing Code, IAPMO and ASME standards. Install it where someone can reach it to clean, and have a licensed plumber connect it to meet local code.
Every shampoo bowl, backwash unit and color bar sink needs one. Mark bowl locations in the salon floor plan maker so the plumber knows where each trap goes.