Liability Insurance Question

[Pete Harper]

I'm looking for advice on liability insurance coverage.  I've posed the same to my insurance broker, seeking a second opinion.  

I currently own a duplex. I first purchase the property in my own name and signed for the mortgage. We were just starting out and I didn't have a credit history in the LLC name. I was able to get better financing terms using my own personal credit. The loan is conventional FHA. About 9 months after closing I was able to transfer title for the property into the LLC. However I could not transfer the loan without refinancing. This leaves me with the property held in LLC name with property insurance and a Million dollar umbrella policy in LLC name. My question is do I carry direct liability exposure from the loan being in my personal name? Can I be sued directly without the LLC to buffer? I carry a Million dollar umbrella policy in my personal name. Will that cover me in the case that I'm sued?

Suggestions on better liabilty coverage?