sowmyancs posted a event handler which shows the name of the user who has created the task, in the “created by” column and if somebody modify that task by approving/rejecting that workflow task, then that person’s name has to show in the “modified by” column.

all the tasks are creating and adding to the Task list under the Application pool identity and that is why we are getting SPWeb.CurrentUser value as “System account”.

See the details here