Yes, you can claim expenses for a vehicle that is not in the business owner's name. The expenses include operating expenses, CCA or depreciation, and eligible interest paid on a loan (if you can prove the taxpayer actually made the payments). This is considered by CRA to be "Beneficial Ownership" and the attached link contains some valuable information.
Be sure to keep your documentation and mileage log available if CRA requests it, and an explanation of your situation.
http://www.taxspecialistgroup.ca/public/taxtips.asp?n=05-27&site=lewisandco
