Yes, you can be an amateur mathematician who manages to avoid such classes and may not know those results or objects, but if you haven't read and written down the name enough to avoid habitually misspelling it, you are outing yourself as a meat proxy unless you are dyslexic.
Mostly we wrote initials in our notes and the exams didn't ask about them. The lecturers only wrote initials on the chalkboard after maybe writing the name once when introducing it the first time. We weren't there to do mathematical history and remember names or something.
Google existed then and now and we could look them up if needed.