If you are working in 'linear' view in the Score, you will need to turn on Global Tracks (View:Global Tracks) to encourage the Score to display the names on the lefthand side. (Note that names are nothing to do with Global Tracks, but that the space on the left where the names show up is "hidden" by default).
If you are working in Page view, the names are displayed according to the 'Layout:Numbers and Names' settings, and also the Score Set.
Thank you for your help, but I'm still a bit confused. I tried global view.
Here's a more specific example of the problem: I have a viola part that is actually named "viola" in the arrange window as well as the mixer window. But when I go to the score editor, the same part is named Instrument 8. I've tried renaming it in both windows just to see if that would help, but it's still showing up in the score editor as Instrument 8. Maybe there's a way to rename the part in the score editor, but I've not been able to do that.