Hello,
1.- You do not say in which context that new feature might be useful. Is that a "student project" or something that would be used in "real life"?
2.- Which question types do you think would need to display respondents' names (apart from those Yes/No and Radio buttons questions on your screenshot?
3.- Which version of Questionnaire would you like to work on? I expect latest one, 2.6.
4.- This new feature might need some significant development, but is certainly quite feasible if you know enough PHP and of course enough of the Moodle API.
5.- The file that would need most changes would be mod/questionnaire/report.php.
All the best,
Joseph