Navigate to Widget Instances, find your widget and then customize the filter builder such that Opened for/Requested for, condition should be set to "is dynamic" and "Me" is set. This will return the currently logged in user = the Opened/Requested for records of your requests.
While in Service Portal, you can also hold Ctrl, right click and then select "Instance Options" and it will open up a dialogue window with the widget itself where you can edit the encoded Query should you wish to do it that way.
