FORT COLLINS, Colo. — The national debate over the use of the term “illegal immigrant,” which has become anathema to people who support relaxed immigration rules, has fixed on an unlikely lightning rod: the liberal-minded, pro-immigrant owner of a Mexican restaurant chain.

The proprietor, Pete Turner, 43, opened his first Illegal Pete’s restaurant nearly 20 years ago, and says that the name was inspired by the name of a bar in a novel and by his late father, also named Pete, who had a rebellious streak. At the time, said Mr. Turner, the word “illegal” held little of the political charge it does today. “I never intended it to be about undocumented immigrants,” Mr. Turner said. “Never. Not once.”

But in opening a new locale here — the chain’s seventh — Mr. Turner seemed to have stumbled on a political tripwire he had not known existed, drawing ire from local and national immigrant rights groups that say his use of the word in connection with a person’s name is derogatory and offensive. Furthermore, they said, they are alarmed that an additional Illegal Pete’s is slated to open in Tucson in August.

“The crux of it is that it’s become a racial slur,” said Cheryl Distaso, 54, one of a group of local residents who are calling on the owner to change the name. Ms. Distaso said she believed that Mr. Turner had not mean to offend anyone when he opened Illegal Pete’s in 1995. “But the impact of that word in this day and this town is different,” she said, “and ultimately it’s the impact of our actions that we’re responsible for.”