The only name I believe to be truly unique that I have ever come across is Chymme. When you google it, the girl I knew is the only person who comes up. But I don't even know if it's a real name or if her parents made it up.
Other names I've come across (not all in real life, some only in books/films/tv) that I'd consider to be highly unusual:
Aphrodite, Aphra, Amity, Amberly, Avril, Athene, Alondra, Andromeda, Ara, Aziza
Bellatrix, Belinda, Belen, Batsheva, Bluebelle
Calliope, Clea, Candida, Clarice, Caprice, Celyn, Carlotta, Christabel, Clemency
Danica, Demelza, Davina, Doria, Dakota, Darina, Devora, Delphi, Dominique
Elora, Elowen, Enya, Evadne, Elisaveta, Elianne, Eugenie, Eriskay, Elektra
Fabia, Fenella, Fiora, Fionnuala, Francine, Flavia, Felicia
Giselle, Ginevra, Guinevere, Genesis
Hebe, Hero, Hera, Hepzibah, Honor, Hosanna
Irona, Ilonka, Isolde, Iara, Ishbel, Irma, Inga, Ivana, Isis, Indiana
Jessamy, Jacinta, Jocasta, Jerica, Joelle, June, Jaime, Jovie, Josette, Juniper
Kerensa, Katinka, Kiki, Keisha, Kiran, Kendra, Keziah
Leticia, Leandra, Liara, Liora, Lettice, Lavender, Laurel, Lowen, Livia, Lux
Mala, Mika, Miranda, Mirren, Mirabelle, Melinda, Marissa, Melisande, Meloney
Nyah, Nerilly, Neriah, Nuala, Nanette, Nicolette, Nadine, Nesta
Ondine, Odette, Odille, Orianna, Oceana
Phyllis, Pandora, Paloma, Psalm, Phyllida, Posy, Pippi, Paria, Philomena
Queenie
Rivkah, Rhiannyd, Rosita, Rosina, Rowena, Raine, Raven, Richenda, Rebel
Samaris, Sixtine, Sephora, Sorcha, Story, Saffron, Samya, Samara, Star
Talitha, Tamika, Tonya, Tansy, Taryn, Trixie, Trinity, Tigerlily, Tatiania, Truly
Una, Ulrika, Ursula, Uma
Vittoria, Veda, Vashti, Viola, Velvet, Valentina, Venus
Winona, Wilhemina, Wilma
Xanthippe, Xenia
Ysanne, Yolanda, Ysabel
Zeryn, Zipporah, Zenobia, Zillah, Zelda, Zia, Zola, Zinnia