By renaming a conversation you're able to find it easier when searching in your chat history. And if the person gets back to you again, in a second conversation, you'll be able to tell who's writing to you.

To rename the conversation, place the cursor over the default name of the conversation – Visitor. This will highlight the word and just by start typing, you will rename the conversation. Press [Enter] to save. You can rename a visitor in the Details field to the right but also at the top of the conversation.