Option "Create a subdirectory for each database" was not check.
"-CrBkSubDir" is missing in the below script.
execute master.dbo.xp_slssqlmaint N'-D "ALL DATABASES" -BkUpMedia TSM -BkUpDB -BkFileName -Logging 0 -CompressionLevel 2 -Default "%D_%T" -NOOPTOLR -TSMConfigFile "C:\dsm.opt" -TSMManagementClass "STANDARD" -TSMObjectPath "fast" -Exclude Offline LogShippng '
Correct syntax would be:
execute master.dbo.xp_slssqlmaint N'-D "ALL DATABASES" -BkUpMedia TSM -BkUpDB -BkFileName -CrBkSubDir -Logging 0 -CompressionLevel 2 -Default "%D_%T" -NOOPTOLR -TSMConfigFile "C:\dsm.opt" -TSMManagementClass "STANDARD" -TSMObjectPath "fast" -Exclude Offline LogShippng '
WORKAROUND 1:
Make sure the "Create Subdirectory.." options is being selected on both "Select TSM Objects" screen and "General Tab: of "Back Up Database Task"
WORKAROUND 2:
On the "Select TSM Objects" screen, Put "%D\%D_%T" in the File format field.
STATUS:
Waiting for fix in a future release of LiteSpeed for SQL Server
