Is it the previous user task you want the name of?  Could you have a hidden field that collects the user name when submitted and would be filled when the next person opens the form?

Yes, that is what I was doing. Using the Current User variable, I was hoping to capture that. But, it does not capture who completed the task, always has the person who initiated the instance.

Thanks

Mine always capture the name of the person working on the current task. For instance, an individual submits an invoice requesting approval for payment.  In this clipshot, I'm on the version of the form the approver would see and it does capture my name each time in this read-only field: 

Try duplicating your form and using the copy as the version that your new user sees when they complete their task.  And build a new single line field to capture that user in.

I usually have 3-4 versions of my form for every process... as slightly different version for each user task (in most cases).

Ok, will try, thank you.

Are you setting the default value of that field to {/_currentuser_display}?