If you want to share site access with an organization that you haven't registered as a partner, that organization won’t show up in your list of options for sharing. Please contact your account manager or support to start the sharing process with this organization.
Sharing is initiated at the default level. This means that your site is shared with all permissions, and the organization appears in your list of known organizations. To limit the permissions, go into the Sites tab in Access Control to assign a role to the organization.