Strategies for teaching with facial aphasia (inability to recognize faces aka prosopagnosia, face-blindness)
Unless it is too embarrassing to you, you might actually consider simply telling your students about your facial aphasia at the beginning of the semester.  You can explain that even though you care about them and know who they are as people and students, you won't be able to recognize them by appearance.  A more familiar condition you might make an analogy to is color-blindness.

You might then ask them to identify themselves by something that you will be able to recognize them by.  For example:


If it's a small class, you might make name tags to sit on students' desks in front of them during class.
In a large class, you might ask students to say their name when they ask a question.


You know your condition best, of course, and what things will work well for you.  You are, of course, admitting a weakness and some of the nastier undergraduates might attempt to use it to play pranks on you or to cheat in some way.  I suspect, though, that at that age in most cases it may be better to play it straight and people will respect you more for doing that than for attempting to hide it.