Well, it's happened before. Marie Curie became very famous for her work in radioactivity. In 1903, Marie and her (much less famous) husband Pierre shared a Nobel Prize in Physics with another, even less famous scientist.
Then in 1911, Marie won another Nobel of her very own, this time in Chemistry for the discovery of two new radioactive elements: radium and polonium. She's one of only four people—and the only woman—to have won more than one Nobel.
Can you imagine how difficult it'd be to be their kid? Mommy and Daddy have three Nobel Prizes between them, and you're supposed to live up to their expectations? Well, not to be outdone, Marie and Pierre's daughter, Irène Joliot-Curie, also won the Nobel Prize with her own husband, in Chemistry, in 1935.
And thus the Curie family name will live on forever as a game-winning answer at trivia night to impress your friends with. Unfortunately for you, the overachieving Curie family are the exception to the rule; generally, nuclear scientists work hard in relative anonymity without seeing their name in the local news.
So if it's fame you're after, check out another occupation; otherwise it's really just going to be you and your nuclei, together forever.