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 “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 the cards. We don’t have a feature that only allows you to see this information.

Also, you can only use the feature "Show card's author" if you're the creator of the board.

In case you're using a team board and you're a team admin of that team, you'll be able to use the "Show card's author" feature as well.