With Fae, Faeryn or Faerune, I would assume you're a fantasy fan, though I guess with your usernames that isn't much of an issue. I think double names could also work.
I think the thing that upset people was:
So, kid can have unusual name, but if kid's well spoken, that's usually all it takes for bully to ignore him/her.
also, when it comes to things bully wants to joke about on something, unusual name is thing bullies pick up last.
and then telling people who've experienced bullying that people just misunderstand jokes - it's a bit inappropriate when someone says they were the victim of bullying to dismiss that out of hand as children joking: the audience decides the joke, not the person who thinks they're a comedian.
Children tend to pick up on the derision from who and what is around them - media, their peers, adults, and so on - so if any of those mock people who are/"act posh" and characterise that by particular odd names or being well-spoken, then yeah, a child who fits that may experience bullying based on that. If the derision is towards people with traits associated with "oiks", "yokels", "chavs", "those who can't take a joke", whatever... what causes a child to target another for abuse depends in large part on the culture around the child. What's easy pickings in one place won't be the same as another.
My DD1 has been experiencing abuse for the way she speaks since Y7 and is now Y9 years now, mostly verbal remarks, having people scream in her face about it, and once being chased home. There was actually an issue at her school for a bit as there was a common idea with some adults that children don't bully for being well-spoken or an American accent and it took her being called a mongrel and that she couldn't be British to get the school to step in properly. The fact it took the bullies moving to xenophobic attacks disappointed me, I'd hope professionals were better trained in this.
Oddly, my DS1 has a stammer, struggles to be 'well-spoken' and that seems like it would be easy pickings -- but he doesn't get remarks about how he talks beyond occasional remarks about his accent (he attends a different school). The things children attack others for varies widely, it's not as predictable as many on baby name threads and even some professionals sometimes think.