The name "Oe" is a Sei (or Honsei) which is a family name representing a large group of blood relatives, such as Minamoto, Taira, Fujiwara, and Tachibana; it is not a Myoji, which is a family name originating from the name of the region from which the person came or the job the person does.
源、平、藤原、橘と同じく姓(本姓)であり、苗字ではない。