That question is best answered by your tax accountant.
For liability exposure, it doesn't matter, if you are the driver and owner.
Tax liability it might make a difference. Company can depreciate against income before taxed. In your name, truck depreciation comes after taxed company income.
Within the LLC and personal tax structure, the income follows thru to the personal income. So it may not make a difference using Federal tax code. Your state income tax may be a little different.