We are already storing that information inside the jBPM Console NG logs. What we are doing is to use the currently logged user and store it in the process execution logs. Then you can query those logs in order to pick up the information about which user started a process. You can take a look at the ProcessInstanceLog class which already has the place to store the identity of the user that is starting the process:
https://github.com/droolsjbpm/jbpm/blob/master/jbpm-bam/src/main/java/org/jbpm/process/audit/ProcessInstanceLog.java
Depending on how you get the currently logged user in your application is how you will fill this attribute.
Cheers