The company has had several strong quarters since his arrival, but in its most recent earnings report, a critical sales growth measure was less than half what Wall Street had expected. The company’s stock has tumbled 17 percent since the miss in late November; Mr. Bogliolo largely blamed weak spending by Chinese tourists, who have scaled back amid a trade war with the United States and a slowing economy at home.

Tiffany hopes to perk up interest in the brand with its program on sourcing. Initially, it will tell customers the country where the diamond came from. In 2020, it will share information about where each diamond was cut, polished and set. Mr. Bogliolo said he hoped to someday be able to provide the name of the mine where it was found, the artisan who shaped its contours and the jeweler who secured it in its setting.

“It’s relevant nowadays for customers,” he said, surrounded by archival sketches and vintage Tiffany jewelry at the company’s headquarters in Manhattan. “Customers are very educated, mature and demanding.”

Tiffany’s efforts to attract younger shoppers extend to the Instagram-ready cafe it opened in 2017 inside the nearly 80-year-old flagship store in Manhattan. Its recent ads have featured Zoe Kravitz, an actress described as “the reigning millennial fashion icon,” and a remix of “Moon River,” the classic song from the 1961 film “Breakfast at Tiffany’s,” performed by the rapper A$AP Ferg and the actress Elle Fanning. At the Golden Globes on Sunday, Lady Gaga wore a custom necklace with more than 300 Tiffany diamonds to collect her trophy for Best Original Song.

Although the company hopes its information-sharing campaign endears it to younger buyers, the initiative has its limits.