No. Since the property is in his name, but you pay the mortgage, he can't take a deduction for mortgage interest, because he is not making the payments.
If your name is not on the deed or the mortgage, you can't deduct the mortgage interest either.
Likewise, neither of you can claim the real estate taxes. Real estate taxes are only deductible by a taxpayer who pays the tax and is legally required to pay the taxes.
Your son does not have to report this as a rental, and he also doesn't have the right to deduct anything unless he is the one who pays the real estate taxes.