Give to me your loving, take from me my name

The story:

I always thought it said "take from me my name", as in "we are going to get married and I will give my maiden name up and take your last name."

I had no idea what the actual title of this song was.

I only realized I was wrong when I heard a radio DJ clearly say "next up is 'Leather And Lace' by Stevie Nicks and Don Henley" and then the song I was already familiar with began to play.