This is going to be high risk, in the unlikely event you are audited. The CC receipt is in your name but the charity acknowledgement is in someone else's name.
The main reason for the charity to issue an acknowledgement is to confirm the money was a charitable gift and not the purchase of some tangible benefit. (For example, if you pay $500 for a charity dinner, of which the fair market value of the fancy dinner is $200, the charity must issue a receipt that the value of your donation is $300. Or if you buy artwork at a charity auction and pay $3000, but the fair market value of the artwork is $2500, your donation is $500.) The purpose of the acknowledgment is to verify that the money reported on the credit card receipt is actually a donation.
Given the above, I would like to think that an auditor would give more weight to your CC receipt than the acknowledgement. However, this situation is definitely an audit risk, and I would suggest you open your own accounts so you get the acknowledgements in your own name.
