We never learn this young man's name, even though he appears at some crucial moments in the story, but the brakeman is closely connected with the book's theme of mystery. When we first meet him, the brakeman is whistling Halley's Fifth Concerto, and inadvertently introduces the theme to Dagny.
"Tell me please what are you whistling?"
The boy turned to her. She met a direct glance and saw an open, eager smile, as if he were sharing a confidence with a friend. . . .
"It's the Halley Concerto," he answered, smiling.
She let a moment pass, before she answered slowly and very carefully, "Richard Halley only wrote four concertos."
The boy's smile vanished. (188.8.131.52-16)
The musical theme is very important in the novel. Dagny hears it in her mind at various points, and it becomes something of a hopeful mantra to her. It's also notable that the boy seems to recognize her as a friend here.
We don't learn until much later the young brakeman's full connection with music: he's actually a pupil of Richard Halley's. So what is he doing working as a brakeman? Well, in Galt's Atlantis, everyone works in whatever jobs are needed and pursue their passions on the side, in the free time they create for themselves. Some strikers also take menial jobs in the real world, in order to avoid serving the looters.
So a musician moonlighting as a brakeman isn't a contradiction in Galt's value system. He's doing necessary work in order to have the freedom to pursue his true passion. The young brakeman also helps demonstrate the connection between the arts and business/science that exists in Galt's system. Since all work is work of the mind, this makes a lot of sense.