I have gotten used to being asked: "So what kind of a name is that?"

My simplest and most accurate answer is "Eastern European."

Pinpointing my heritage gets difficult in light of a few name changes. Take my dad's side of the family. Mildred Walker, my paternal grandmother, was born Carmella Vaccaro. Her family, who were from a town called Lungro in Calabria, Italy, became the Walkers in the United States.

She led her life as Millie Walker until she married Wasil Smerconish, whose family came from somewhere in Austria-Hungary. His name had been changed from Smerakanich. Still, the census takers couldn't get it straight. In three consecutive censuses beginning in 1900, it was recorded as Smerakowitz, Smerakanos and Smerkovitch.

Mom's side is more straightforward. The Grujichiches were from Yugoslavia. But they, too, changed - to Grovich - when they passed under Lady Liberty. And there is hardly anything unique in that. My family's willingness to change their name was just part of their assimilation process, one that began at Ellis Island.

But today I see evidence of that process in retreat, as the Smiths, Jones and Wilsons are quickly being displaced by the Garcias, Rodriguezes and Martinèzes.

A recently released analysis of U.S. Census data compiled in 2000 found that we have to change our ideas (if we have any) about what constitutes an "American" surname. Among the most common surnames, two Hispanic names - Garcia (No. 8) and Rodriguez (No. 9) - cracked the top 10, a first according to many demographers. Martinèz advanced eight spots to No. 11, barely behind Wilson. (The data made no distinction between those here legally and illegally.)

The influx of Hispanic names has been swift: Between the 1990 and 2000 census analyses, Garcia jumped 10 spots, while Rodriguez moved up 13. There are six Hispanic names among the top 25 - double the number in the previous compilation.

The increased frequency of Hispanic names is, no doubt, due in part to unprecedented immigration. An analysis of census data conducted by the Center for Immigration Studies revealed that 10.3 million new immigrants have come to the United States over the last seven years - more than any other seven-year period in our country's history. It is estimated that more than half came illegally.

Today, 1 out of every 8 people living here is an immigrant - good for an estimated total of almost 38 million.

That many of those 38 million are arriving with their names intact may illustrate the main difference between today's immigrant and those who arrived at the turn of the last century.

The Smerakowitz, Vaccaro and Grujichich families arrived prepared to do whatever it took to be "American," even if that meant updating the spelling of their names every 10 years. While they did not forget where they came from, they were anxious to follow immigration laws, to learn the English language, and to become a legitimate, moving part of the economy. The result was the oft-cited image of the United States as a melting pot.

But today, we've stopped melting. Or as former presidential adviser and candidate Pat Buchanan recently told me: "The melting pot is cracked and broken."

What has changed? The issue is not that too many Hispanic names are finding their way over the border. It's what happens - or doesn't happen - once they arrive.

I know I'm not alone in my belief that today's immigrants - those here both legally and illegally - are not assimilating the way my forefathers did when they arrived.

And before I'm shouted down as a xenophobe, hear me out. My intent isn't to amplify the shrill debate surrounding illegal immigration. What I'm interested in is defending the tradition to which my grandparents adhered: the one that led them to a new name and a better life in this country.

I fear we are leaving it behind.

Something else Buchanan told me struck a chord.

"We all want to be proud of our ethnic groups," he said. "It is when we diverse people became one new people that we became strong, that we became Americans, that America became great.

"It is when we came together as one that we became a united and great nation. So . . . I'm not denying people the right to their roots; they ought to be proud of them. But we ought to celebrate the fact that we are a new nation, one nation, one people, we are Americans."

He's right. And it's the reason I find no fault with those who want the same for the Garcias as we did for the Grujichiches. And the Vaccaros, as well as the Walkers.

Michael Smerconish's column appears on Thursdays in the Daily News and on Sundays in Currents. He can be heard from 5:30 to 9 a.m. wekdays on "The Big Talker," WPHT-AM (1210). Contact him via the Web at http://www.mastalk.com.