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That seemed to happen in one of my grandparents' families: Robert's son William had a son Robert who had a son William ... who named his first son Robert, second son John, known as Jack, third son Edward, known as Ted. Then young Robert died. Their next child was a daughter, my grandmother, and then finally there was another boy who was named Robert. He named his only child William, but that William and his wife didn't have children so the chain was broken.

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In your scenario, if I was very close to my grandfather I think I'd use his exact names: Eli Isaac. And I'd explain to little Eli Isaac exactly what would be expected of him one day!