These are the names of children where I teach that I have never met another one of - or not in recent years at least. (terrible sentence!) I haven't included names that are only so unusual because of their spelling:
Girls: Aliya, Anastasia, Amreeta, Annalise, Athene, Camilla, Caprice, Cathy, Celest, Cerys, Christabel, Clare, Fenella, Fionnhuala, Gemma, Iona, Jaskiran, Juliet, Katinka, Mira, Meg, Nayana, Nyah, Pippa, Rosemary, Sadie, Samai, Samya, Sorcha, Zia
Boys: Alejandro, Arnav, Ayrton, Barnaby, Benedict, Craig, Cosmo, Diego, Douglas, Ferdi, Fitch, Gennady, Gregory, Guy, Hal, Hector, Joleyon, Keshav, Monty, Nelson, Niall, Nacho, Oluwakorede, Oluwatoni, Orlando, Orson, Paris, Peter, Rafi, Ranulph, Rex, Ruan, Shea, Simon, Tasimba, Tavish, Tawanda, Teo, Tolulope, Vishal
Some of those might not be unusual names in other cultures or countries at all, I don't know.