Docker Inc. on Tuesday named Mike Gupta, the former CFO of Twitter Inc., as its chief financial officer, signaling a greater interest at the business software company at finding ways to make money.

Although it got off to a slow start, Docker’s growth exploded in the last year or so after the company started offering open source “containers” that let software applications run unchanged across multiple environments, making it much easier to develop and run software in the cloud.

Docker...