Unique means one of a kind. When it comes to names, that sets the bar pretty high. Just ask the 123 parents who named their children Unique last year. (Can you imagine going through kindergarten as Unique H.?)
Finding a truly one-of-one name would mean opting for something that might not be very name-like at all. Draxlee, maybe. Or Porcelain.
Instead, most parents try to strike a balance between the often-heard and the less familiar. If that’s your mission, moving beyond the most popular 1000 names in the US might be enough to satisfy your craving for the uncommon.