how to enable this function to display the group image or name?

Can you please clarify what you are asking? The image shows a Topic, but it appears to be the Topic List view. All info available by default is already showing there.

What is it you want to appear, and where exactly?

Mark… I think he’s asking how to show that a staff member replied inside the thread. In this case, the IPS team badge being shown in the screenshot. 

This would be the "Highlight items with replies" member group setting. That is showing our group icon.