A clear majority of Hispanics living in the United States say it's important for their community to have a national leader. But they haven't decided who should have that title.

The top two names mentioned in a new Pew Research Center survey of Hispanic adults in the U.S. were Supreme Court Justice Sonia Sotomayor and Sen. Marco Rubio (R-Fla.). But each of them were named by only 5 percent of respondents when asked an open-ended question.

More than six in 10 (62 percent), meanwhile, said they don't know who the most important leader in the country is today. The two other names mentioned often enough to register in the survey were former Los Angeles mayor Antonio Villaraigosa and Rep. Luis Gutierrez (D-Ill.).

It's notable that Sotomayor, who is still pretty new to the Supreme Court, has cut a national profile among Latinos on par with Rubio, who is often seen as the country's highest-profile political figure. A New York City native, Sotomayor is of Puerto Rican descent. Rubio is Cuban American.

Even as Hispanic Americans have have not reached anywhere near consensus about who their most important leader is, they believe it is important to have one. Ninety-one percent of respondents said it was    "extremely," "very" or "somewhat" important.

One other interesting finding in the poll: Half of respondents said they have no preference between the terms "Hispanic" and "Latino." But about a third said they prefer "Hispanic" while 15 percent said "Latino" is preferable.