Here are the steps you need to follow to see the card's author name and to see who commented on your card.
Step 1. Click on the clockwork icon (settings)
Final Step. Now select the “Show card's author” option
Note: Once the “Show card's author” option is checked everyone is going to see the card's author name and who commented on your card. We don’t have a feature that only allows you to see this information.
Also, you can only check the option "Show card's author" if you're the creator of the board. In case you're using a Team board and you're an admin of that Team you'll be able to use the "Show card's author" option as well.