Moving A Sent Message

When I move a message from the ‘sent’ folder to a folder that I need it to. The sender’s name changes to mine.

You are the sender of the message.

In the Sent folder it is not showing the sender, because all messages are from you. Instead it shows the recipient of the message.

Similarly in other folders it is pointless to show the recipient of the message, because that is you. So in folders where received messages are, it shows the sender.