If you make a donation in someone else's name who gets the tax deduction?

Presuming it meets all the things to be deductible, You do. You gave it. (You can't deduct from taxable income, income you never brought into taxable income...so for the other party to deduct it, they would have to first include it in income and then give it, (which of course you couldn't deduct because they aren't a charity)).