Is it possible to merge multiple organizations within Zendesk Support?
No, it is not currently possible to merge organizations within Zendesk Support.
However if you are on the Professional or Enterprise plan, you do have the option to add users to multiple organizations. For more information on this feature please see, Enabling multiple organizations for users (Professional and Enterprise).
Another alternative would be to create a new target organization for your users. Once you have the target organization setup, you can run an API call that updates the desired users organization to the target organization. Please note that this update will not change the organization on any tickets that are in a Closed status. For more information on using the API to update users please see our developer doc, Create or Update Many Users.