Renamed issue types like stories or epic(managed issue types) get overwriting  on the destination site in some cases. For reference: How Jira Cloud Migration Assistant links your data

For instance, suppose you have two instances: Instance A (source) and Instance B (destination). In Instance A, you've renamed the issue type "Story" to "User Story".

When migrated to Instance B, which already has a "Story" issue type, it will get overwritten by "User Story", not creating a duplicate but replacing the original.

So, it will be good if JCMA could provide a list of the changes that will be made in the issue types. After the approval, the user should proceed with the migration.