It is either you do it manually as you need to open each result file to check the source field. (I know it is hard to manage in this way).
Or you need to process each audio file separately : 1 file = 1 batch transcription job
and you can assign a unique display name to each job.
Links to hep you :
https://learn.microsoft.com/en-us/azure/ai-services/speech-service/batch-transcription-create
https://learn.microsoft.com/en-us/azure/ai-services/speech-service/batch-transcription-get