Landlord Insurance and Umbrella Insurance

[Carlo D.]

Had a question for the experts here. 

When you get liability insurance for your rental property.  I'm assuming you get landlord insurance and Umbrella Insurance.  My questions were a few fold:

1. For Landlord insurance, other than coverage for the property, does it also cover you from potential liability from your tenant?

2. Do the policies have to be in the LLc's name? (the LLc that holds the rental property) Or.. particularly for Umbrella, can you just add the property as part of the insured locations in one's existing personal umbrella policy?

Thank you in advance.