George Bernard Shaw's play Pygmalion has been adapted many times for different media, but most notably as a musical entitled My Fair Lady. This musical was so popular that some screen adaptations have used the title "My Fair Lady" instead of the original "Pygmalion".
Why was the title changed to "My Fair Lady"? Is there any connection with the nursery rhyme "London Bridge is Falling Down" which is often also called "My Fair Lady"?