I'm in San Luis Obispo County and I'm supposed to post a copy of my Business License which states that I'm authorized to collect TOT. As for the business entity, it just has my name and the type of business is Vacation Rental.
Since I don't ask guests to pay the TOT separately (it's just included in my nightly price) I don't post it.
I imagine that the business entity is you but perhaps you should ask the City sending you the notice how you're supposed to fill it out. Most governmental agencies are new to the Airbnb thing and haven't updated their instructions. They just want the tax!
Hope this helps a bit.