You can already do this.
Add the Org.
When creating an entry, add the desired org name to the entry.
From here you have a few options depending on your specific needs.
You can use the organization filter shortcode option to display a list of users assigned to a specific org like so:
[connections organization="My Org Name"]
You could turn on the org name linking feature on the Connections : Settings admin page under the Advanced tab. With this on, the org name for every individual will now be links. When a user clicks that link, they will be shown a list individual assigned to the org.
Another option is to link directly to org lists; like so:
http://my-domain.com/directory-home-page/org/My Org Name You can even add this links as custom links to your WordPress nav using the Menu editor.
Hope that helps.