For our BBs, stripes are embroidered, so only about 1/4" wide, and some people have belts with their names embroidered on them, which usually have Roman numerals instead of stripes. I have one of each, but I usually only wear the one with my name on it for events, like tournaments and testings, where I wear my best dobok (the one that's middleweight instead of lightweight and doesn't have sweat stains on it); I wear the one with the stripes for instructing and working out.
To make it easier for students to differentiate between ranks, I Dan through III Dan have white stripes, IV Dan through VI Dan have gold stripes, and VII Dan through IX Dan (our highest rank) have red stripes. Which belt people wear (with stripes only or Roman numerals with names) is up to the person wearing the belt. My embroidered belts were all gifts from my sahbum, and I follow the same tradition, buying embroidered belts (one with the name and one with the stripes) for my own students. The only exception is I Dan, who get one plain black belt and one with their name and a Roman numeral. I also have a plain black belt for when I visit other classes; as a visitor, I am always junior to that instructor's BB students, no matter our relative ranks, unless the instructor chooses to place me elsewhere relative to his/her own students' ranks.