Parents giving their children unusual names is fine but there's one rule which seriously should be enforced: No names based on adjectives or objects. Unusual names are all well and good so long as someone hears it and thinks "I've never heard a name like that before." not "That's something you'd find in your backyard! Why would you name your kid, or any living thing for that matter, after that?" For this reason names like Apple or Moon Unit would be outlawed. Apple's not so bad but Moon Unit?! Seriously, I know it makes his name Moon Unit Zappa but come on! That's not a person's name! It's not like your making funny names in your character profile for WOW or something. This is a real person and they'll live through their entire childhood with that name. Do you actually want your kids to stand out and be pointed at? What, having a famous father isn't enough? They've got to have a flaw of their own on which you can blame their social issues rather than their relation to you? And it'd still be your fault anyway. This is why "You can change it later" is never a good excuse, kids are brutal. They'll take the name "moon unit" and use every bit of their imagination to come up with jeers, insults and pranks to put him down and make him feel out of place.
I like unusual or interesting names, that's why I thought it was brilliant that David Bowie named his kid Zowie but I cringed when I found out Jermaine Jackson named his kid Jermajesty. What the hell?! And it was a boy too! As if that kid wasn't gonna grow up with enough of an ego...