A selection of poke, a Hawaiian dish of seasoned raw fish, at a supermarket in Honolulu. A Chicago-based poke chain sent cease-and-desist letters to other restaurants using “Aloha Poke” in their names.

Aloha Poke Co., a Chicago-based restaurant chain, has been fighting to protect its trademarked, Hawaiian name for more than a year. It was not until this week, however, that the backlash to its efforts drew a public apology from the company.

Though its name is Hawaiian, the company is not. The restaurant, which sells poke, a Hawaiian dish with seasoned chunks of raw fish, usually over rice, was founded in Chicago in 2016 — the same year it trademarked its name. In the months since, Aloha Poke has sent cease-and-desist letters asking businesses with similar names to find new ones.

Reports of the letters sparked outrage and accusations of cultural appropriation. The flames were fanned this week by Facebook videos — including one from the Hawaiian physician and activist Kalamaoka’aina Niheu, which was viewed tens of thousands of times — and an online petition that gathered more than 25,000 signatures. It said the company had “aggressively threatened Kanaka Maoli (Native Hawaiian) families with legal action.”

People in Hawaii were upset by the news, Kaniela Ing, a Hawaii state representative who urged people to boycott the company, said on Tuesday.

He said it was especially ironic to see “aloha” at the center of such a controversy because the word is representative of Hawaiian culture and can mean many things, including hello, goodbye and love.

“It’s hard to define,” Mr. Ing said. “But I can say what it’s not: It’s not suing other people for…