The only way I know of currently is to submit the second request under a different user's account!
You may create a dummy user with one or more responsibilities and initialize the environment to use this one right before you submit the request.
One of the way is to create a new responsibility and before submission of concurrent program, do apps_initilize with the new responsibility name.
By this way you would see only the first request id.
Bear in mind that if you do hide it and the program fails, how is your user going to see why it has failed?
However if you do want to do this (and assuming you are using forms rather than OAF to view conc requests) then my suggestion would be to personalise the FNDRSRUN form if possible to add in a default where clause. Submitting as another user programatically would probably work but you could end up in a whole heap of problems down the line as things change.