AP IMPACT: NYPD shadows Muslims who change names

Taking an Arabic name might be a sign that someone is more religious, Brown said, but it doesn't necessarily suggest someone is more radical. He said law enforcement nationwide has often confused the two points in the fight against terrorism.

"It's just an example of the silly, conveyor-belt approach they have, where anyone who gets more religious is by definition more dangerous," Brown said.

Sarah Feinstein-Borenstein, a 75-year-old Jewish woman who lives on Manhattan's Upper West Side, was surprised to learn that she was among the Americans drawn into the NYPD program in its infancy. She hyphenated her last name in 2009. Police investigated and recorded her information in a police intelligence file because of it.

"It's rather shocking to me," she said. "I think they would have better things to do. It's is a waste of my tax money."

Feinstein-Borenstein was born in Egypt and lived there until the Suez Crisis in 1956. With a French mother and a Jewish religion, she and her family were labeled "undesirable" and were kicked out. She came to the U.S. in 1963.

"If you live long enough," she said, "you see everything."

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