The Japanese casual-wear retailer that is a subsidiary of Fast Retailing is Uniqlo.
Uniqlo began in 1984, when Tadashi Yanai opened a unisex casual-clothing store in Hiroshima called Unique Clothing Warehouse. The name was later shortened to Uniqlo; a “C” was reportedly misread as a “Q” during Hong Kong registration, and Yanai chose to keep the spelling.
Fast Retailing became Uniqlo’s parent company after changing its name from Ogori Shoji in 1991. It also owns brands such as GU, Theory, and J Brand, which explains a common mix-up: GU is a related Fast Retailing label, but it is not the answer to this question.
Uniqlo is known for relatively simple, practical clothing and product lines such as HEATTECH. Its name is often expanded as a contraction of “unique clothing,” while its corporate parent is Fast Retailing Co., Ltd.