My three daughters all had names that were unusual at the time, though one of them was subsequently popularised by a character in a soap. They girls all really love their names.
My sons have classical names, not terribly unusual, but no other boys at their schools shared their names. Nowadays the name of my youngest son has gained in popularity.
My name was a real source of angst when I was younger. My paternal grandmother was Lilian, my maternal aunt was Lily and so I was named Lillian. It just didn't fit! I never felt comfortable with the name and even other people used to comment that it didn't suit me, so I happily swapped it in my early teens for my very plain and unremarkable middle name, which does suit me and by which I've now been known for almost 50 years. Oddly enough in the last few years I've made my peace with the name; it's still my name on all 'official' documents, at the health centre, the bank etc., which I used to resent, but now I don't mind owning the name.