Wow, I came to this thread hoping it would already have an answer.  The feedback module is practically useless unless this is changed...

Thanks, DV.  I actually did figure that out, and I suppose I should have wandered back here and said that was my solution, so thank you also for the reminder.  I know how, but did not want to modify the database so that it might save the name... but I figured that the "name" was linked to the name of the DNN user record, not the DNN feedback module.  I didn't look into that but I suppose it makes a kind of sense.

I also modified the input template, so now my "subject" is actually "display name" so that people will know they can enter a public name to be displayed; I figured the subject of the message wasn't crucial.

Moreover, from the Issues log, there doesn't appear to be any activity, or any recognition of this basic bug.