(CBS News) The question WHAT'S IN A NAME is no idle question for anyone born with a very famous one. Just ask the woman Mo Rocca tracked down on her own home turf:
Ah, the life of a Rockefeller. All a child could ever want, or so it would seem . . .
Eileen Rockefeller showed Mo Rocca a photograph taken of her when she was about two. "One of my favorite pictures of me . . . I was just kind of like this, reaching out."
"What was the two-year-old Eileen Rockefeller saying in that picture?" Rocca asked.
"Hello, somebody! Come play with me," she sighed.
A little girl who just wanted someone to play with.
You could say it's the theme of a new book by Eileen Rockefeller, a rare inside look at growing up as part of one of the country's wealthiest and most powerful families.
Her great-grandfather was John D. Rockefeller, Sr., the founder of Standard Oil . . . and America's first billionaire.
Eileen's father was David Rockefeller, who ran Chase Manhattan Bank. He gave her a name to be proud of . . . and a name that could inspire dread.
She writes that being a Rockefeller filled her with gratitude and anxiety.
"Well, the two go hand-in-hand, just like opportunity [and] obligation," she said. "And there are enormous opportunities and gifts of huge abundance in being a Rockefeller. And ironically, all of us have also experienced scarcity.
"But it's not scarcity of money. It was scarcity of attention, scarcity of time. Because with a very busy family, busy parents, there is a lot going on. And with six children, less time to spend with each of us."
Eileen, the youngest of six, says her parents were so busy being, well, Rockefellers, that she never got enough time with them. Her older siblings often ignored her.
Problems plenty of kids have, sure. But most of them don't have that name.
She told Rocca that when roll call was read in school, "I wish I could have hidden under my desk. My hands were always sweaty, but that's what it is."
And then there were the questions from other kids.
"I mean, they would ask things like, 'How many houses do you have?' 'How much money do you have?' "
"Really? Well, that's amazing," said Rocca. "Well then, can I ask you, as a journalist, how much money do you have?"
"I have no idea," she laughed. "I don't even count."
"Is it more like Powerball money, or more like Mega Millions? I'm kidding you, I'm joking with you," Rocca said.
"Get out of here!" she laughed.
Rocca visited the Rockefeller family compound in Maine, where he joined Eileen and her father for a carriage ride.
David Rockefeller is now 98 years old -- the last of his generation. The trails they rode were laid out right after World War I, almost a hundred years ago, by his father.
"They were built by Father," David Rockefeller said. "He loved riding and he went driving every day really, except Sundays, when he was up here."