In sent message, the user name is not displaying
This is currently working as designed. The message listings do not show your own username as you obviously are a recipient as it is displayed for you. It is however a limitation of the current system that when you send a message to yourself, no recipient is shown.

You can alter the sql query and remove the exclusion of the current user for the sent list, but then it will always show the current user there.

There are some ideas on how to make the whole listings more flexible but that's quite a bit of work and needs time that I currently don't have.