Apologies for any repeats. Names I'd think of as fairly unusual:
Arwen, Ayla, Anya, Aria, Ada, Astrid, Avril, Adele, Aubrey, Agnes, Belen, Bonnie, Briley, Brenna, Corinne, Colette, Crystal, Callie, Cassie, Carrie, Claire, Clea, Dana, Diane, Dulcie, Elin, Enya, Effie, Etta, Fallon, Farrah, Giselle, Gemma, Helen, Harper, Hayley, Hadley, Hero, Hebe, Ines, Iris, Jade, Jayla, Jada, Karen, Kayleigh, Kelsey, Lois, London, Lyla, Lyra, Marnie, Monique, Morgan, Nora, Nyah, Nia, Orla, Odette, Paula, Peyton, Presley, Paisley, Piper, Rita, Rowan, Romy, Ria, Star, Sasha, Susan, Sian, Tarryn, Tansy, Vashti, Willa, Xanthe, Yvette, Yvonne, Yasmin, Zia, Zelda