All cash property, should I set up a trust?

I purchase a property all-cash with my own name. I would like to have it in an LLC, but it's just not cost effective as it's in California and the $800 annual fee would kill my cash-flow. Would it be beneficial to drop it into a trust even if the closing took place in my name? It would seem that I would still be easily discoverable as the owner if it was closed in my name previously. I've read through other forum posts, but couldn't find a definitive answer.