I understand where you're coming from, ex L.A. Lakers and Oakland Raiders. However there are many other examples of teams being able to change their name and survive even given the same circumstances you mentioned before... for example, Baltimore Ravens, Washington Wizards (a team that went through 4 name changes), and the Kings.
The Jazz didn't change their name and built a brand here in Utah. I guarantee if they would have changed the name it would have been a brand that we would all know and recognize since the move. The Stockton-Malone era was the era that sealed the Jazz brand name in Utah.