The Name is Lightning II:

The Air Force has chosen the name Lightning II for the new F-35 Joint Strike Fighter, announcing the choice at a special ceremony at the Fort Worth facility of prime contractor Lockheed Martin on July 7, 2006. Air Force Gen. Michael Moseley, who made the final selection, told attendees from Congress, industry, DOD, and the program’s eight partner nations, that the name was a “win for aviation heritage and culture.” Lockheed Aeronautics President Ralph Heath said the name recalls the P-38 Lightning of World War II fame and the British Lightning supersonic jet fighter of the 1950s.