What is needed to conduct business in another state?
Unfortunately, you will not be able to avoid the pesky $800 California franchise tax so long as you want to do business in California. There's no problem in starting your company in Wyoming, but doing business in Nevada in California. In fact, Wyoming is a great state to form your LLC.
Once you form your Wyoming LLC, all you need to do is register as a foreign entity in each state where you wish to transact business (other than its home state of Wyoming). As I've mentioned, unfortunately, California will right away start charging you the $800 franchise tax once you register the foreign entity. There's no loophole to work around that.
A DBA is a different concept, and it doesn't apply to your situation. It would apply if you wanted to do business under a different name, not just in a different state.