Is there a way to put a time stamp with the users name into an adjacent cell when a cell is updated?

In case that didn’t make sense I will tell you what I need this for. We are creating new time cards that require both employee and manager approval on them. We have many remote employees and getting their signature can be a pain. If they could click a button on the time card that stamped their name and time that would be ideal. They would then send to their manager they would click to verify the time and it would stamp it as well.