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You don't need to put the car in your LLCs name to take deductions, and by doing so it may screw with your insurance premiums. Check with your CPA and your insurance company
My CPA and another third party CPA recommended having company name on the title so that we are covered during an IRS audit. While taking insurance, we have to explicitly mention that we are going to use car for business commute and not for transporting cargo/people etc. I did this while taking MX insurance with GEICO and my insurance premium is normal range.
As far as liability is concerned, as my company is LLC, I believe I would be fine. It would be a different scenario, if its a Corp. This is my limited understanding though !!