When one talks to Peter Poopat and Flavio Girolami, it is easy to forget that they are the design duo behind the label Common Projects, the super-minimalist sneaker worn by everyone seeking a hint of upscale cool, from the creative layman to Kanye West.

It’s also easy to forget because Mr. Poopat, 43, and Mr. Girolami, 42, would like you to. “It sounds silly, but we rarely tell anyone we just met what we do,” Mr. Poopat said.

He’s not exaggerating. While vacationing last July in Ibiza, Spain, with his wife and two children, Mr. Poopat was introduced to Amir Kassaei, the chief creative officer at DDB Worldwide. When Mr. Kassaei asked about his profession, Mr. Poopat answered innocently that he had a company “and we make shoes.” It was only when Mr. Kassaei pressed further that he coughed up the name of his global brand.

“Amir immediately jumped up and turned to my son and said: ‘You know who your father is? Your father is my hero. I have 50 pairs of his shoes,’ ” Mr. Poopat said with a laugh.