Are the alms given to a trusted person for distribution among the needy, with some of the needy and the distributor knowing that they are from the giver, considered a secret or a public charity?

You will be rewarded for your charity whether people know about it or not, and whether they pray for you or for your representative. A secret charity is one that only Allah knows about. Since some people knew about your charity, it is a public charity. This does not harm you as long as you seek the countenance of Allah through it. The majority of jurists have held that declaring obligatory charity is better than concealing it, and that the verse: {If you disclose acts of charity, it is well; but if you conceal them and give them to the poor, it is better for you} [Al-Baqarah: 271], was revealed concerning voluntary charity.