When the Approver completes his approval process then the Admin needs to close the document by selecting the Closed value in the Document Status field.
My problem starts from now:
When the Admin Selects the “Closed” option from the Document Status field the value in the Application Approver field changes to the name of the Admin (Who will be a diffrent preson from the Approver) and the Approver name is wiped off from the Application Approver field adding the Admins name in it.
No, you will not get desired results even if you change the field to Computed when composed.Infact in that case the approver value will not set at all since record would have saved once earlier.
The problem is with your condition,
It checks if status is “Approved/Not approved”,then capture the name of current user.
When admin is saving record ,he meets the condition in formula so previous value is overwritten by new value.
Instead you can check if the value of the field is “”,then proceed ahead