Karl Lagerfeld’s death leaves a void atop two of fashion’s biggest names, Chanel and Fendi, and signals a potentially seismic shift on the industry’s creative side at a time of heightened flux in the global luxury market.

Chanel has already named Virginie Viard, a relatively unknown company insider based in Paris, to continue Mr. Lagerfeld’s work. Ms. Viard was the director of the Chanel fashion creation studio and Mr. Lagerfeld’s right-hand woman for more than 30 years.

At Fendi, where Mr. Lagerfeld was named creative director in 1965, the question of succession has not yet been addressed beyond a company statement that a decision on the issue would come “later.” Nor has there been any word about Mr. Lagerfeld’s own brand, which he started in 1984 and which is now partly owned by the private equity firm Apax Partners.