I am getting a RLI personal umbrella policy from an independent insurance broker.

We discussed this with our agent, and they recommended a traditional rental policy with an umbrella policy. 

I'd have an umbrella liability policy. 

@Ryan SummersNo matter what California is going to get you whether your LLC is in California or notMy recommendation just buy in your name and get an umbrella policy

LLC does not protect much  better  to also have Land trusts and umbrella policy

Not that it is quite the same but my umbrella policy provider stopped covering vehicles in CA.  

Each of us take out an umbrella policy in our name own names, or what would your advice be?

Umbrella insurance may be a better way.

If you don't have significant other assets to protect, it's probably easier and cheaper to just get an umbrella insurance policy.

In regards to your question about renters insurance I always require tenants to have it and maintain it.As far as your other questions some people go for an LLC to protect their assets (but more work to do tax time to do it right) where others keep it in their name and get landlord insurance and/or umbrella insurance.