Ms. Kennedy, who declared last week that she would like to succeed Hillary Rodham Clinton as the junior senator from New York, is in many ways embarking on a test of the enduring power of her politically royal name.

Interviews with about 50 New Yorkers — people from upstate and across town, people of all ages and races and political persuasions — suggest that the Kennedy brand is rich with resonance. But it also provokes resentment and puzzlement, especially among younger voters, who are suspicious of dynastic politics as the Bush era ends, and are uncertain of where in the famous family tree she falls.

“I don’t know who her father is, but if you told me, I bet I would know,” said Michelle Kuhns, 21, a senior at St. John’s University in Queens who was working during her holiday break at a bagel shop on Long Island. “I’ve heard the name, yes. But that’s it.”