What's in a name? Gulf of America? Mexican America?

MEXICO CITY — At her daily news conference, Mexican President Claudia Sheinbaum on Wednesday displayed a colonial-era map of North America — with much of what later became the United States still shown as part of Mexico.

“América Mexicana,” the president said, suggesting that the entire region revert to the 17th century classification, which translates to “Mexican America,” shown in the map. “That sounds beautiful, no?”

It was a sly jab at President-elect Donald Trump — who a day earlier suggested that the Gulf of Mexico be renamed the Gulf of America.

“What a beautiful name,” Trump said. “And it’s appropriate.”

Trump’s proposed geographic switcheroo was greeted with widespread derision in Mexico and throughout Latin America.

“Obviously, the Gulf of Mexico is recognized by the United Nations,” Sheinbaum said, rejecting the notion that the signature body of water—which has born Mexico’s name since colonial times — be rechristened.

But Sheinbaum, a scientist not known for her sense of humor, wasn’t done. She also adapted a playful tone to take issue with another Trump assertion.

He claimed that Mexico “is essentially run by the cartels. … Can’t let that happen. Mexico is really in trouble. A lot of trouble. Very dangerous place.”

“With all due respect,” Sheinbaum said, the president-elect had been misinformed.

Trump, Sheinbaum suggested, was apparently under the impression that the country was still being run by ex-President Felipe Calderón and his former security chief, Genaro Garcia Luna, the latter now serving a 38-year U.S. prison term for collaborating with the Sinaloa cartel.

“But, no,” Sheinbaum said. “The people govern in Mexico.”

Special correspondent Cecilia Sánchez Vidal contributed to this report.