Umbrella insurance for rental property

[Inessa Bliznetsova]

Hello, I hope someone has experience with this and can help me with this question:

I own a condo in USVI in my own name, which I occasionally use for myself and family, and the rest of the time it is a vacation rental (well, was before COVID, now it's more 1-6 month rentals. I have declared to insurance company that i do so, and have liability insurance with them, but it is capped. I thought that my umbrella policy that I personally have, covers the rest - but I was told by Allstate agent that it does not include rental property. This was news to me, because my neighbor in NY who has  rental property here in NY said that he keeps it in his name and has umbrella to cover excess liability.

I would appreciate any insight into how people handle rental properties when they are in their name.

Best regards,

Inessa