Current State:

Currently, Jira admins can only add existing users with visible email addresses (according to Update your profile and visibility settings) to the Organizations in Jira settings:

• Settings > Products > Organization (https://<sitename>.atlassian.net/jira/settings/products/servicedesk/organizations)

For Organization administrators with verified domains, they can only search for users whose emails match their domain. This means that if you manage accounts across multiple domains, you won't be able to search all of them.
 

Proposed Future State:

The suggestion is to allow Jira admins to search for all users on the site.

Workaround:

Add customers to Organizations directly from the project, following our documentation