I suppose I should first start off that I begin to get nervous when 'unique' starts getting paired with 'name' because I have nightmares of of weird letter substitutions or multiple consonants for aesthetic purposes rather than any grammatical or pronunciation reasons. There are other weird instances where characters have quite a mouthful of 'unique names' as a given name and suddenly it's Starrlytte Kheeara Eve and I don't know what to think.
Names that are appropriate to the setting and story of the book are best, for me personally, without sounding too grandiose. That's why the characters in Harry Potter work - nothing in those books is decided upon without a reason, and JKR did her homework to the last letter - for me but the name Bella Swan gave her kid doesn't. The names Neal Shusterman gave the characters in Bruiser are unusual, but for what's happening in the book they make complete sense and actually help to convey a part of the personality. Same with Alaska Young in Looking For Alaska - she is such an outgoing, vibrant, and slightly untouchable spirit that for her to have a name like Jane Smith would never have worked in the same way.
I guess my point is that I don't look for unique names at all. I just hope the name choice suits the overall environment of the book. :)