I am not aware of any law that would prevent the charity from giving either the donor’s name or the amount of the gift to the family who recommended the memorial gift to the charity.

Unless the donor specifically asks to remain anonymous, I assume that most charities will tell the family the name of the donor so that the family can also acknowledge the gift and say thank you.

Whether you tell the family the amount of the gift may depend on what you do generally with reports of other donations.  Do you have a privacy policy that could affect the answer?  If you are an organization that puts out an annual report listing donors by giving category, such as those giving between $75 and $149 in one category and those giving between $150 and $399 in another, etc., it would not seem to make much sense to withhold the number from the family if the donor will be publicly listed later in one of the categories. 

If you don’t list donors at all, or list all donors without regard to the size of the gift, you have a decision to make.  Will you interfere with the donor’s relationship with the family if you report a gift of $5?  Do you want to list all givers in a group with the total amount of the gifts but single out those who have given a more substantial gift, over $300, for example.  If you spoke to the individual’s family prior to their recommending gifts to your organization, what did you say about making the amounts known?

Ultimately, I think this is a public relations question, not a legal one.  Much of the readily available commentary on the subject says it is “best practice” not to disclose the amount of the gift to the family, but a best practice is not usually a legal necessity.  I would be interested in hearing from other readers how they handle the situation, and why they do what they do.