You do not see a "relate" tab in the CI tab ? You can use this to relate one or more existing CIs and the all the fields should be displayed like CI Name, location etc (If defined). The upper box is for CIs used by organization and the lower one is for the role for that CI.
I understand what you want. You want the "CI view" on the organizations to display "searchcode".
Well, here, the view defined as "default" for configuration items is used for presenting "CIs" on the organization form. I experimented by adding some fields and removing some others. The changes appeared also on the organization form.