Answer:
The Titans were renamed to the Jets for two reasons 1) playing at Shea Stadium and the nearby La Guardia Airport. and 2) It also kept with the rhyming theme with their neighbor (at the time), the Mets.
The rhyming theme was also involved in the renaming of the NY Americans (ABA) to the NY Nets (now NJ Nets).
Only thing I can think of is that Shea Stadium opened in 1964. They had to notice the noise from nearby La Guardia airport when Leon Hess bought the Titans from Harry Wismer and was looking to rename them.
I'm somebody who has a different thought: For fans of the Tony-Award winning and Academy-Award winning musical, "West Side Story", the street gangs fighting each other are called the Sharks and the Jets. It takes place on the West Side of New York City. Hence, the New York Jets. What do you think?
I really think it was from the musical "WEST SIDE STORY". When the movie came out it was huge. It made quite an impact on the nation, specifically New York. Which I believe matches the time frame the JETs were named.