When we download a CSV of issues, the columns export as what seems to be key Data, this is evident in the Organizations field (which is also denoted as Custom) it displays a Number as opposed to the Customer's name which is displayed in the search prior to the download, This is also the case in many other fields.
There are 3rd party custom field types (an in this sense Organization is a 3rd party custom field type, as it is offered by Jira Service Desk, not by Jira Core) that are not exported correctly. What you see in this case is the ID of the organization, not its name.
I'd check if the Jira Cloud REST API (especially the end-points offered by Service Desk) can return the organizations. I'd expect this is supported.
Then you could look up the organization names by knowing their IDs at the cost of some extra programming.
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