Drop in on one of Peloton’s cult spinning classes on any given day and you’re bound to see sweat-glistening instructors with abs that could cut glass. Oh, and a middle-aged man named Brad.

The 42-year-old Brad Holcman, who works at a New York television network by day and spins under the username #BradNeedsAbs, has quickly become one of the most recognizable figures in the world of stationary-bike maker Peloton. And it isn’t because he’s employed by Peloton (he’s not) or because he’s a fitness model (he’s not).

Instead,...