This is a myth that has been around a long time…perhaps as long as people have been shaving. However, the answer is no; shaving doesn’t change the thickness, rate of growth, or color of your hair. This is because shaving has no effect on the hair follicle that grows the hair.
Shaving does give hair a blunter tip than the typical tapered end of a longer hair. This makes it feel more “stubbly” as it grows out but doesn’t change the thickness. So don’t worry about making your hair thicker or darker by shaving.