No, Gerald Ford's real last name wasn't even Ford. He was adopted by a couple with the last name Ford. His birth name was Leslie Lynch King, Jr and was legally changed to Ford when he was 13.
Henry Ford II is Henry Fords Grandson. He was also known as "HF2" and "Hank the Deuce". HF2 was appointed head of FMC after the Death of his father Edsel Ford (HF son).
There is no relation. His birth name was Leslie King. When his mother got divorced and married Gerald R. Ford (not the president), he eventually adopted his stepfather's name. I find that odd...but...