Can I list donors' names in my app to thank them for donations made externally? Will my app pass Apple's review process if I list the names of donors in my app?  I don't have any link to donate in the app, and there is no way for users of my app to donate in the app.  All donations are handled externally.  Donors do not get any additional features.

Donations are not to a charity or non-profit.  My app is free.  Would the answer be different if any of these were not the case?
Yes, it turned out you can do this.  I submitted by app to the App Store and it was approved.  Apps cannot have a link to donate, but they can list donors' names.

If you are a registered non-profit, you can put a link to your site to donate in your app.