As a Jira user currently it is not possible to identify what is the Program in which a work item is part in Jira Align.

Customers value this information in Jira Align Features mainly (Jira Epics)

In the screenshots below we have the Project name in Jira, and there is no sync of the Program field, which exists in Jira Align

if the users don't have access to JA, they would not be able to know the Program, by doing the correlation which exists