Hi, is it allowed to deduct expenses for use of a car that is not registered under your name? Thanks.

“Hi, is it allowed to deduct expenses for use of a car that is not registered under your name”---> In general, you can deduct the business-use portion of your car expenses on your tax return; for example, even if you lease a new car for use in your business, you will probably be able to deduct the lease payments from your taxes as a business deduction. However, you need to be careful and keep track of all the miles you spend in the car and whether the miles traveled are for business or personal reasons. If it is not for this case, then NEGATIVE.

Did you keep a contemporaneous written log of ALL miles driven, including personal, commuting, and business? If not, your allowable business use deduction is $0.
Commuting costs are NEVER deductible regardless of the distance. That's true whether you are an employee or are self-employed. You can take a business use deduction of either the actual cost of operation of the vehicle, apportioned for the business use or take a deduction of 50¢ per business mile driven, again according to your written log.