Is it permissible to take an undisclosed commission from those participating in the Eid Udhiyah (sacrifice), such that they believe it is being paid to someone else, to cover the costs of searching, purchasing, and supervising, in addition to my contribution of a share?

It is not permissible to take a commission without the knowledge of the one who pays it, because it is a type of ja'alah (stipulated payment for a service), and this requires an offer and acceptance. It is not enough to inform subscribers about the amount of the commission without telling them that you are taking it for yourself, because they may accuse you of betrayal if they come to know the reality of the situation.