DESCRIPTION:
From wikipedia:

"Woman" is a 1966 single by Peter and Gordon, written by Paul McCartney under a pseudonym.

Under the Lennon--McCartney moniker, McCartney had written three previous Peter and Gordon singles (viz. "A World Without Love", "Nobody I Know", and "I Don't Want to See You Again").

On this occasion, McCartney used the pseudonym Bernard Webb (though some Capitol pressings carry the name A. Smith instead) to see if the song would be a success without the Lennon--McCartney credit. McCartney commented at a press conference in August 1966,

"People come up to them and say, 'Ah, we see you're just getting in on the Lennon--McCartney bandwagon'. That's why they did that one with our names not on it... because everyone sort of thinks that's the reason they get hits."[1]

However, the publishing credit was Lennon and McCartney's company Northern Songs, and according to Gordon Waller it took only two weeks' time for the song's real author to be revealed, as the first review of the record said, "This Bernard Webb has an amazing talent. Could even be Paul McCartney!"[1]

It was then introduced as written by McCartney when Peter and Gordon performed it on the US TV show Hullabaloo.