The problem is caused by some conflict in the ibus input method management system, especially when adding Korean as an input method to ibus (package ibus-hangul). By disabling ibus, the problem went away. So it appears that ibus IM, especially with Korean, is conflicting with nemo's ability to right-click rename (rename works, but you can't see the text) and renaming more than one file in list view (which breaks nemo completely until you log out and back in again).
The problem is caused by some conflict in the ibus input method management system, especially when adding Korean as an input method to ibus (package ibus-hangul). By disabling ibus, the problem went away. So it appears that ibus IM, especially with Korean, is conflicting with nemo's ability to right-click rename (rename works, but you can't see the text) and renaming more than one file in list view (which breaks nemo completely until you log out and back in again).