
Originally Posted by
Puglife
Matsudaira was the actual clan name, and Tokugawa was the name used by the Shogun and his main heir. The other children of the Shogun were Matsudaira, and the Aizu domain belonged to a direct offshoot of the Shogunate. The "Tokugawa crest" is actually the Matsudaira clan crest, and since the Aizu Matsudaira were true Matsudaira, part of the Shogun's extended family, they would certainly have used the clan crest.
Sometimes non-relatives were allowed to use the Matsudaira name as an honorific as well, but the Aizu family was truly Matsudaira, directly descended from Ieyasu. It gets a bit confusing because Ieyasu's biological grandson was adopted out of the family, and then later "reclaimed" by later generations and allowed to use the Matsudaira name again, but biologically the Matsudaira blood was unbroken, IIRC, and they only spent a very short time using a different name and crest.
Hope that helps!