Are you aware that "Hey Jude" was written by Paul McCartney for John Lennon's son Julian?
Mainly because in 1968, John Lennon and his wife Cynthia Lennon separated due to fact of John's affair with Yoko Ono. Soon afterwards, Paul McCartney drove out to pay a visit to Cynthia and her and Lennon's son, Julian.
McCartney thought that they've been very good friends for millions of years and it was a bit much for him to be suddenly personae non gratae.
Cythia recalled that it was truly a surprised when McCartney arrived in their house one afternoon on his own. Cynthia was truly touched by McCartney's concern for their welfare. In his journey down, McCartney composed 'Hey Jude' in the car. She will never forget Paul's gesture of care and concern for coming to see them.
The song's early and original title was 'Hey Jules' and it was intended to comfort Julian Lennon from the worries of his parents' divorce.
Mccartney recalled that he started with the idea 'Hey Jules', which was "Julian, don't make it bad, take a sad song and make it better. Hey, try and deal with this terrible thing."
He knew it was not going to be easy for Julian. He always fell sorry for kids in divorces. He had the idea by the time he got there. He change it to "Jude" instead of Jules, because he thought that it sounded a bit better.
Meanwhile, Lennon's son Julian realized that the song was written for him almost twenty years later. Julian recalled of being closer to McCartney than to his father; "Paul and I used to hang about quite a bit more than his Dad. They had a great friendship going and there seems to be far more pictures of me and Paul playing together at that age than me and my Dad." [source]