Zipgrade is an app for grading multiple choice responses. It is free for the first 100 uses per month and not expensive for unlimited use. Answer sheets in a variety of sizes are able to be downloaded from here. Student ID can used on the larger question response forms. I have even used the 100 question form printed 4 to a page without issue.
There’s the ability to import student names via a csv file and to likewise export the results. Marking is almost instantaneous when you line up the squares on the scan area with the black boxes in the corners of the student response sheet.
All response sheets are recorded for future consultation and analysis of the results is made. My trial quiz had 5 questions all with answer A. Notice how my response sheet with 10 answers scanned. I deliberately tested having 2 answers for question 1.