Should I leave them in personal name and put a umbrella coverage on them ?

So before accommodating new tenants, we are planning to take tenant's insurance coverage.

@Maksym Chernov just get a standard commercial fire/liability insurance policy with $1M coverage (this is likely what the insurance company will require).

@Henry Clark and @Mike Lambert - Good points, comprehensive analysis, and nice theoretical and paper exercise but I would like to share with you my practical experience of living and investing in Latin America and Europe.Whenever you are investing overseas, you need to consider in your analysis 2 major risks: FX/currency and regulations.

It's worth it for me to pay 10% for eviction coverage, tenant screening, not having to answer the phone at 2am, not having to schedule showings, etcetera. 

Flood insurance is 2-3x more expensive than regular coverage.

Insurance is only there to cover what's damaged so you need extra coverage.

@Pride Davis so in that case it would probably do more harm than good because you would now have the added expense for extra coverage which in turn would cost the consumer more on top of the increased interest rate.

The other thought was to get an umbrella insurance policy instead for this 1st rental and possibly either expand the $$ coverage when additional rentals are paid off or then setup individual LLCs for the multiple rentals. 

The transfer from you to the entity is considered a sale and you're original policy could easily decline coverage when you need it most.