@Tigryapa in between when other users updates the forms, is your workflow executes "Update Item" or "Set Field" value actions?

@kunalpatel  my workflow is triggered by status on an item (i.e. ready for review). Once the item is in this status, the workflow starts and moves according to what users input on the form. For example, if user updates the form with certain value, it either closes workflow as completed and sends email to originator or if user chooses different value, the status of an item is updates and email is sent to other user to do a second review. At the end of each workflow the last two actions is set status = completed and notification sent to initiator 

@Tigryapa your users are updating the item so at that time it will show their name in modified by field. But, then the workflow is moving forward and updating the item also and since the workflow is running under initiator's creds, it will update the modified by field with initiator's name. You can create another field where you can capture last modified by name via workflow and also the modified field and keep appending with old values, that way you can have an audit trail you want.