Currently, when the customer permission to share request is restricted to Other customers in their organization. This option only allows them to search for customers in their organization the user picker filed works as expected. On the portal, the user picker field is limited to the members of the customer's organization:

However, when an agent tries to report a request from the portal on behalf of the same customer, the user picker list is no longer restricted to the customer's organization but all customers.

As an Administrator, if we have multiple customers with the same name working in different organizations, to avoid issues we need a filtered user picker. Also sometimes the agents will be raising the request on behalf of the customer's, in that case, it gets more difficult to find the correct approver since there will be customers listed outside the customer's organization too.