Pantone. The world’s only universally accepted color communication language.
Virtually every color-dependent industry (from product design, fashion to software development) employs PANTONE Color product development specifications.
For screen printing, Pantone has laid out all the colors available by name and formula. Each ink system has its own set of formulas based off the basic colors in said system. This allows you to mix any color in the Pantone Matching System. (PMS)
Many companies will trademark or register their logos. In doing so the colors of those logos are logged and assigned the appropriate PMS number for printing. As a printer it is your job to match your ink to this number/color.
The Pantone Solid Coated Book is the universal book for the printing industry. If you do not have one of these books it is recommended you have one in your shop.
Most customers are fine with Scarlet Red, Royal, Blue, etc but for those that are more specific being able to offer any color int he rainbow can set you ahead of the rest.