I would need more information to accurately answer this question and would likely want to see a copy of the applicable insurance policy. However, generally, if a person is a "named insured" on an insurance policy, that policy could cover that person/entity in the event of a covered loss under the applicable insuarance policy. Feel free to contact me for additional information. Thank you.
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It is possible that you could have a cause of action, even though Florida is an at-will employment state. You would have to determine who reported the false report to unemployment (your employer or the testing agency), how it was reported, and who is responsible for the wrong report being attributed to your name. I hope this helps.