Children usually just accept names - they rarely have the associations that we have with a name.
Also, the being bullied bit is bullshit. It's true people may be bullied about their name, but it's just as likely that this bullying situation would have occurred, anyway. But perhaps the bully might have chosen the colour of their coat to pick on, instead. Children with perfectly ordinary names may also be bullied. ("Luke Puke!" for example.)
The "we're in London, so we're open minded" bit is is crap, as well. There's as many closed minded bigots in London as anywhere else - more, because the population is greater than in other places. (And I live in Greater London, for context.)
What I don't get is that Caspian is apparently a "mumsnet name", whereas Florian is "wet". 
In short, OP, call your DC what you choose. Only really rude people will make a comment about a name, when introduced to someone of that name. And, to be fair, I agree with Lweji that the posters here are commenting on names in the abstract, not on a particular person's name.