Minamoto no Yoshishige (+1202), grandson of Minamoto no Yoshiie (1041-1108), was the first to take the name of Nitta. He sided with his cousin Minamoto no Yoritomo against the Taira clan (1180) and accompanied him to Kamakura.
Nitta Yoshisue, 4th son of Yoshishige, settled at Tokugawa ((Kozuke province) and took the name of that place.
Yasuchika (1369-1412), son of Chikauji, took the name of Matsudaira. He was in charge of Iwatsu castle, then of Okazaki castle, and strengthened the authority of his family in the Mikawa province.
Ieyasu (1542-1616) descended from Yasuchika in the 7th generation. In 1567 he obtained from the Emperor permission to revive the name Tokugawa. In so doing, he claimed descent from the Minamoto clan.
The clan rose to power at the end of the Sengoku period, and to the end of the Edo period they ruled Japan as shoguns. All in all, there were fifteen Tokugawa shoguns. Their dominance was so strong that some history books use the term "Tokugawa era" instead of "Edo period".
In addition, the heads of the gosanke (the three branches with fiefs in Owari, Kishū, and Mito) bore the Tokugawa surname. Additional branches became the gosankyō: the Tayasu, Hitotsubashi, and Shimizu Tokugawa clans. Many daimyo with the Matsudaira surname were descended from the Tokugawa. Examples include the Matsudaira of Fukui and Aizu. Members of the Tokugawa clan intermarried with prominent daimyo and the Imperial family.
Tokugawa's clan crest, known in Japanese as a "mon", the "triple hollyhock"(although commonly, but mistakenly identified as "hollyhock, the "aoi" actually belongs to the Birthwort Family and translates as "Wild Ginger" - Asarum), has been a readily recognized icon in Japan, symbolizing in equal parts the Tokugawa clan and the last shogunate. In jidaigeki, the crest is often shown to locate the story in the Edo period. And in works set in during the Meiji restoration movement, the crest is used to show the bearer's allegeance to the shogunate -- as opposed to the royalists, whose cause is symbolized by the Imperial throne's chrysanthemum crest.