Is it obligatory to specify the name of the person on whose behalf the sacrifice is made when participating in a share of the sacrificial animal? If so, does any guarantee or obligation fall upon the one who participated on behalf of another without specifying the name?

It is permissible to purchase an udhiyah bond from charitable organizations as an agency for slaughtering, and this is valid if the organization designates the owners of the udhiyah, such that it has a list of the sacrificers' names and slaughters the specific udhiyah for each of them. It is not valid if the organization does not designate the owners of the udhiyah, but rather slaughters a certain number of animals for a certain number of people without specifying the particular animal for each sacrificer. This is what Sheikh Ibn Uthaymeen warned against.

If the designation was not made, there is no guarantee for the past udhiyahs, and the matter of their acceptance rests with Allah. However, it is not permissible to repeat this act in the future. If a flaw occurred in the designation, the responsibility lies with whoever neglected the designation, but the reward will reach the sacrificer, Allah willing.