I believe the Display Field that ArcMap determines to be the default is based on this sequential logic:
First field of type Text whose name contains the word "name" (case-insensitive)
First field of type Text
First field of an integer type
First field of any type
I think the label field ends up being whatever the Display Field ends up being. So are you asking how to set the Display Field for a particular layer within ArcMap? What is the reason for wanting to change a label field in Model Builder? I'm not sure if that can be set using Model Builder, and after looking at the arcpy capabilities for layers within a map document I'm almost certain you can't set this even through a stand-alone Python script.
