I've had both.
My first Karate school used a single white stripe for shodan, and gave you an additional stripe for each rank beyond shodan. We were a poor school, and used medical tape as our stripes.
My Tae Kwon Do school used plain black, no stripes, but once you became Jogyonim (or higher), you could get your name embroidered (in Hangul, as best as the translation would allow) on one side.
My next Karate schools used plain black, no stripes. Those who were Renshi or greater, would get their names embroidered on one side (in Katakana), and the name of the system embroidered (in Kanji) on the other, and those same individuals had the option of using different colored (red and white) belts during formal events.
My current school uses no stripes, but you are allowed to have your name embroidered (in Katakana) on one side, and the system name (in Kanji) on the other side. One yudansha's belt is indistinguishable from another's, except for the name. That, and the amount of wear and tear...