When a report is written to the JES output queue, JES assigns the job name based on the attributes of the task or job that created the output data set. In this case, since the creator of the output is CA Dispatch, JES assigns the CA Dispatch started task name as the job name. Unfortunately, there is nothing that can be done on the CA Dispatch side that would force JES to alter this behavior or to assign the original application's job name to the output dataset.
One suggestion that may help customers facilitate the identification of reports distributed by CA Dispatch and relate the output back to the original application job would be to assign an EXTERNAL WRITER to the CA Dispatch output, that reflects the applications original job name.
You can define the applications original job name as the external writer by using the WRITER field on the "VRDMU130 - Report Recipient Definition screen".
There are other fields available on the recipients VRDMU130 screen such as the FORM or FCB fields that you may also be able to use, that would allow you to associate a CA Dispatch output dataset back to the original application job.
The REPORT NAME may also be of use for identification purposes and can also be assigned as an external writer on the CA Dispatch output dataset by exploiting the WRITER field on the VRDMU130 screen. Or, by implementation of Special Feature 27 (FEAT027) - CHANGE DEFAULT WRITER TO REPORT NAME.