On the chat_queue_entry record, the activity shows the same name and same timestamp. It shows the same name even though the conversation happened between two users and the same timestamp.
The reason is that the chat_queue_entry table is not audited. When the table is not audited, the activity logs will not show the correct information.
Enabling auditing will show the correct activity going forward.
Link to the documentation:
Even after enabling the audit, if a record is created from the chat, all the chat messages will show the same timestamp which can be tracked via problem PRB1040914