If a person giving charity cannot conceal his name, is it permissible for him to say, "Someone gave this to me to donate," without mentioning the name, and would that be considered a lie?

Concealing voluntary charity is better than disclosing it, unless there is a benefit in disclosing it, such as people following suit. If the giver of charity wishes to conceal his charity, he can use allusions (tawriya) and equivocations (ma'areed), such as saying: "This money is not mine," intending that it is Allah's money, or "This money belongs to one of the charitable givers," intending himself, because lying is forbidden.