There is a SoDo (as in South of Downtown) district in Seattle - south of where the Kingdome used to be. (Part of the theory was that the acronym referred to South of the Dome, but that never really seemed right, even when the dome was there.) But by the time the name was used there, it was also used in lots of other places, including some not especially noted for their downtown areas (Orlando, Florida, say). And places much noted for them, such as the most famous of all in New York City.
A few years ago, a substantial commercial development was launched in Boise, also called SoDo (and also, properly, just south of downtown). [UPDATE: A commenter correctly notes that the Boise area is usually known as BoDo, but the other nickname has cropped up occasionally as well.)
Point being, there are SoDos all over the place. So why is the near-downtown area in Spokane, working to build a unique identity, fastening on SoDo to identify itself?