It becomes very clear after reading this excellent short story that one of the central themes is the class system that assumes such importance in English society. Trevor is a name that clearly indicates this character is from the middle classes, and this is something that the working-class boys that make up the Wormsley Common Gang find laughable and ridiculous. Note how this is indicated in this second paragraph of the story:
There was every reason why T, as he was afterwards referred to, should have been an object of mockery--there was his name (and they substituted the initial because otherwise they had no excuse not to laugh at it), and the fact that his father, a former architect and present clerk, and "come down in the world" and that his mother considered herself better than the neighbours.
Trevor's real name therefore signifies the class that he comes from and the kind of upbringing that he has had. The way that the gang stands for the destruction of everything to do with the class system says a lot about Trevor's motives for joining the gang and his own frustration and anger at what he has experienced. Trevor's name therefore is very important in the story to introduce the theme of class and the way that it is so divisive in society. It is important to consider how the destruction of Old Misery's house, and various references to it throughout the story as standing up like a "top hat," play into this theme.