Interestingly, I know online a family who adopted an older girl. I was very excited for them as their daughter was near the age my DC1 was when adopted, and it isn't common for older chilren that age to get adopted sadly
Anyway, their DD's name was the kind of 'classic' name you get often on the baby names forum here. Imagine a name such as Amelia, Charlotte, Harriet, that kind of thing
She decided she wanted to change her name so she could have a fresh start after a really hard time in FC. Her parents said, okay, what name would you like?
She picked 'Diamond' to be her new name, and so it was changed. She and her parents are delighted with it. It suits her.
But I can just imagine the responses were it a Mumsnet thread!! I think some of the people who knew them were surprised or shocked
So there you go. Older children can generally choose, and sometimes they go for unusual names. My own DD1 changed both middle names. Both middle names are taken from a book she loves very much. Her first name, unchanged, is both beautiful and unusual. I wouldn't have chosen her name for a birth child, as lovely as it is (even though I prefer unusual/uncommon names too), but it suits her and is perfect