It's an interesting question considering that you're in West Hollywood. As I understand it, the recent change in LA applies to the City of LA. I wonder if that flows down to WeHo.
In any event, if you are subject to the new L.A. Occupancy Tax situation, my understanding has been that even though short-term renting remains technically illegal in most circumstances, a business license (somewhat misleadingly named "City of Los Angeles Tax Registration Certificate") is required. From the fine print on the back of the license card: "This business tax registration certificate ... signifies that the person naemd on the face hereof has fulfilled the requirements to collect[] ... from transients the Transient Occupancy Tax." Remember that even though Airbnb will be collecting and remitting the Occupancy Tax, they are doing it *on YOUR behalf*.