CaptainNancy - Nooo, I definitely haven't got five children!!! 
It occurs to me reading this that it's so not about what you call them. I would never, ever announce their names with 'pride' or wait for an amazed response. I'm more likely to be apologetic and say 'well it's a bit odd but' or 'we sometimes regret it!'
It's just about whether I like the name and it feels right. Not showing off.
but there are parents who genuinely seem to believe their child is special - I don't think mine are, well not to anyone but me, and my family of course - yes they are great but so is every other child in their class. They're ALL unusual and unique and special.
I really would never want to make them 'stand out' either. Really I wouldn't. I want them to have friends, and to be happier than I have ever managed to be, and to be accepted.
There are a lot of unusual names in their classes and tbh I think a lot of parents do want to choose something that won't be replicated too often by other parents, well at least not among their school friends.
Some people have chosen lovely classic names that they clearly just love, and other people have chosen something more leftfield that they also love. But loving the names seems to be the strongest reason for choosing them, whether they are Zahra or Alfie-Jay.
It's part of the fun of having a baby, to choose something you just really like....like you choose what colour to paint your walls, or what type of coat to wear. There's nothing wrong with it.