Who has their black belt embroidered and why?

i do itf tkd and i see all my black belts have their names and stuff written on their black belts, but none of the red belts have it. how come that is? if you get your belt embroidered, are you supposed to get roman numerals or dan stripes to indicate your level? how come if you get dan stripes on a black belt embroidered, the color belt stripes are pieces of tape? i am so confused....