Hi Amber. I agree with Karin that this is a question best answered by your insurance carrier. But I can tell you that I have an LLC as well, and what I’ve done is had both the LLC and myself personally covered under the same policy. My thinking is that it’s better to be safe than sorry. Check with your carrier/agent for the answer to your question.
I hope that this helps.
I would be more concerned with whether your are insuring a gym or a studio, or whether you are a mobile trainer.
When I secured my space the insurance broker wanted to know the they of equipment I would be using at my studio, whether I had a AED among other question.
From my experience, the focus was not on whether your are sole proprietor, LLC or an S corp or C corp.
As has already been mentioned, what is important is that you speak with your broker.