The fire motif that goes throughout the book draws parallels to ancient myth. Jaunt discovers his ability when he's set on fire and needs to be put out. Gully space-jaunting when he's burning in Old St. Pat's. Fire is the catalyst in all of these things—mirroring both its role as a chemical reaction, and its role in Greek myth, where most prominently Herakles ascended to Godhood on his own funeral pyre. It's through fire that man ascends, it is the catalyst of change. Gully's first act as a thinking being is what? Creating fire in Nomad's engine to free himself. And how does Gully figure out how to space jaunt? When he's caught in an explosion of the meaningfully-named PyrE. In fact, fire is at the heart of Gully's final speech: "Take a war to make you spend. Take a jam to make you think. Take a challenge to make you great." It takes great stress—which is essentially what fire is—to create change. Further, Gully giving PyrE to the people at the end parallels Prometheus, giving the fire of the gods to the common man.
When the name "Geoffrey Fourmyle" first appears, it's in a scenario in Foyle's mind, so the reader naturally assumes he subconsciously chose a name that sounds like a fancier "Gully Foyle". Later, though, we find out it was a default name that Dagenham didn't bother changing. So why does it sound like Foyle's name? And since it does, why on earth would Foyle be dumb enough to use it as an alias?