Ah, I assumed we were talking about Details view before. In List view you can't resize the columns by dragging but you can still resize them, or set the auto-size option, via folder formats.
Go to Tools -> Folder Options.
On the Columns tab you can set the width of the Name column. That width will apply to List view as well.
On the Display tab you'll find the auto-size option.
For help making the changes permanent, see the Folder Formats FAQ.