“We embrace our differences, whether they be race, gender, sexual orientation or belief systems,” he said. Mr. Luis added that while Tapestry was currently composed of brands based in the United States, he was open to acquisitions in Europe and Asia.

To that end, the name was also intended to clarify the differences between not only Tapestry and Kors but also Tapestry and potential European competitors like LVMH Moët Hennessy Louis Vuitton (the owner of brands like Vuitton, Dior, Givenchy and Fendi, and the world’s largest luxury group by sales), Kering (Balenciaga, Yves Saint Laurent and Gucci, among others) and Richemont (Chloé, Alaïa, Cartier and Van Cleef & Arpels).

“I’m not here because I’m anyone’s son,” Mr. Luis said by way of example — an apparent veiled swipe at François-Henri Pinault, the chief executive of Kering, whose father, François Pinault, founded that group.

Then he said, “We are not a group that believes there is a single country where products have to be designed or manufactured,” a reference to the insistence by European groups on the importance of origin — that there is equity in “made in France” or “made in Italy.” Finally, Mr. Luis said Tapestry would include the results of each of its brands in its annual reports, as opposed to lumping them together into a single entity, as LVMH and Kering do with some of their brands.

Still, Tapestry is following in Kering’s steps in at least one way: In 2013, the French group, too, changed its name (it had been PPR), to reflect its transformation from retail and luxury to a luxury and sports lifestyle group.