BCC'S ON EMAILS I SEND SHOW IN MY INBOX AS COMING FROM THE PERSON I SENT MY EMAIL TO, INSTEAD OF THE "BCC" PERSON

I am sending emails from email account user name "Goldberg" to email account user name "Smith", with a BCC to "Goldberg". However, when the BCC appears in my Thunderbird Inbox, under the "From" column, it will say "From Smith" (the name I sent the email "TO", instead of "From Goldberg" (the BCC name)