You do not need to order new DMV documents with your new address, so you just have to wait for the ID that is already on the way.
In addition, I need to learn more about traffic tickets. If my name has changed and I have pleaded no contest to one or more traffic tickets.
the DMV will send you a Notice of Hearing to you with your previous name
If my address has changed and I plead not guilty to one or more traffic tickets