I can only see the message sender's name, not address! And why is Thunderbird calling me "You"?
By default, if the sender, CC or BCC's address is in your address book, Thunderbird will display the person's name but not their email address when you view a message. Similarly, rather than showing your name and email address, Thunderbird will display "You".
To disable this behavior, select Tools > Options (Windows) or Thunderbird > Preferences (Mac and Linux). On the Reading & Display page, un-check "Show only display name for people in my address book".
If you like having the display names but not the "You", install the add-on found here.