I just realized that I'd neglected to factor your grandfather into the equation.
Okay, once more...
When your grandfather (Frank Eliot, Sr.) dies, your father (Frank Eliot, Jr.) then moves up to being Frank Eliot. Your oldest brother (Frank Eliot, III) then becomes Frank Eliot, Jr. And your son remains Frank Eliot, II. If your son should have a son and both your father and oldest brother are still living, then your son's son would be Frank Eliot, III.
But if all the Frank Eliots (including your grandfather) are still alive at the time of your own grandson's birth, then your grandson would be Frank Eliot, IV.