Is it permissible to pay the expiatory alms for an oath (kaffarat al-yamin) – which is to feed ten poor persons – to an organization? And if permissible, what is the name of the organization that does this in Riyadh?

There is no objection to paying money to one of the charitable organizations to feed the poor as expiation for an oath. This falls under the category of permissible delegation. We do not have knowledge of the organizations that do this in Riyadh, as the website is not specialized in Saudi affairs.