Last March, when Tina Sharkey stepped down as CEO of Brandless—a maker of inexpensive foods and household items bearing generic labels like “Avocado Oil” and “Dog Shampoo and Conditioner”—she explained the move by saying she wanted to “wear fewer hats” at the company and focus instead on being its public face. 

But Ms. Sharkey also left the top job at Brandless amid tensions with the company’s most prominent investor, SoftBank, which was pushing for the young retailer to turn a profit, according to a person familiar with the matter. The situation came to a head in a January board meeting where directors told Ms. Sharkey that the retailer was burning cash too quickly. Ms. Sharkey and the board agreed that the company needed to hire an experienced retail executive, another person with knowledge of the discussions said.