These are names I really like that are neither popular nor obscure:
Astrid, Ariel, April, Angelica, Anoushka, Aria, Bryony, Bronte, Cassidy, Cassandra, Christabel, Daphne, Erin, Ebony, Effie, Etta, Fenella, Faith, Fallon, Giselle, Hannah, Iona, Jessamy, Juniper, Johanna, Juliet, Kayleigh, Kyra, Lara, Lyra, Leona, Miranda, Mila, Miriam, Nia, Nyah, Naomi, Natasha, Nicole, Polly, Quinn, Rhiannon, Robyn, Romilly, Rowena, Rowan, Sadie, Saskia, Savannah, Taryn, Thea, Veda, Xanthe, Zia