Andy Dunn, the founder and then-CEO of menswear company Bonobos, declared two years ago that big companies were nearly incapable of creating cool online brands aimed at millennials.

Then a funny thing happened: He sold Bonobos to Walmart last year and became responsible for doing just that for the world’s largest retailer. At Walmart, Mr. Dunn is now a senior vice president of digitally native vertical brands, a clunky title that makes him the retailer’s pointman for cultivating product brands that grew up mostly online, like the young customers who tend to favor them. In his new role, Mr. Dunn figures out whether Walmart should acquire those brands, as it did recently for a plus-sized fashion retailer, or build them from scratch, as it did with a mattress brand that competes with the better known Casper.