The BG_DETECTED_IN_RCYC does not actually contain the name but the ID as Jan indicated. You could however get the list of ID from the CycleFactory of a certain Release.
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Example from API Documentation: ("Get filtered releases under a specified folder" example)
Set FolderFilter = relFactory.Filter
RelName = "Release*" 'Release 1, Release to QA, Release1.1, and so on.
'Get the list of the Releases in the folder that
' match "Release*"
FolderFilter.Filter("REL_NAME") = RelName
Set listOfReleases = FolderFilter.NewList
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You could get the ID list also using the API's Command object and running SQL something like below:
SELECT RCYC_ID, RCYC_NAME FROM RELEASE_CYCLES WHERE RCYC_NAME like '%UAT Test%'
This list of IDs could be then used in API filter.
Note: usage of Command object is only allowed for admin users by default. This can be change by Site Configuration however.