Agent Listed on Text/ Message Thread

Those with teams using Messaging simultaneously with multiple conversations at one time. On the list view of all messages, possibly next to the sourced number the message is attached to, can we include what person/agent is actively engaged in the conversation?  It is listed in the conversation history but to see who at first glance is what we need.   With new incoming messages an agent is not listed (also indicating unread) and once replied to that agent is then listed. For outbound messages, the agent who sent the message is listed.  If there is a new message but from a person who we have spoke with before, the agent who last spoke to them would be listed, but still marked  new/unread.