If a charitable donation was made by a group of
people in someone else’s name as a gift to that person, can this donation be a
deduction on the tax return of the person who was named on the donation or on
the tax returns of those who made the gift, or can no one can claim this deduction?
The people who made the donation get the tax deduction for it. The contributor would need a receipt from the charity in order to deduct it. We actually have an article with a little optional video on just this topic.
https://blog.turbotax.intuit.com/deductions-and-credits/give-the-gift-that-keeps-on-giving-1099/
Let's say a group collects donations in cash, they are given to a member of the group, and one person makes the collective donation to the charity on behalf of the group. (Ex: Sunday School class collects money for a local charity, gives to a member of the class, they write a check to the charity for the total amount of the donations). On the check, it indicates that this donation is on behalf of a group, but it does not clarify anything other than the group's name. How does that work?
Also remember that you need to itemize to claim any charitable deduction. Since the 2017 tax law changed the standard deduction (that you get without itemizing) typically to $14k each person (Single, or joint filing) and limited state and local tax deduction to $10k max, very few people now itemize. [46 million in 2017 to an estimated 18 million in 2018. That is only 10% of filers.] https://taxfoundation.org/90-percent-taxpayers-projected-tcja-expanded-standard-deduction/
That may or may not apply to you, but if you don't itemize (and 90% don't) then the issue is moot.