That's a standard Mac dialog...
Grab the right edge dividing line on the Name column label and drag it to the right.
Thanks, but I am supposed to resize the column EVERY time I open a file from inside InDesign? The windows don't work that way for other apps, even other CS6 apps.
I'm a Windows user, so I can't tell you why it doesn't stick after you adjust it, but I've moved this into the genral discussion so you might get a better answer.