Sorry for any repeats, just brainstorming:
Not too out there but not too popular. Some not used much for a long time:
Amy, Avni, Alba, Asia, Asha, Anya, Ayla, Ailsa, Aphra, Autumn, April, Amber, Astrid, Agnes, Aya, Ada, Adele, Anouk, Aroush, Ama, Billie, Bronte, Brodie, Bridie, Brenna, Belen, Bethan, Brielle, Bridget, Bronwen, Bertha, Carys, Cerys, Ciara, Carmen, Cecille, Celine, Celeste, Claudette, Cora, Coral, Clarice, Caprice, Cherry, Dana, Demi, Delphine, Deirdre, Diane, Dora, Denise, Donna, Elise, Effie, Enya, Etta, Enid, Esther, Eilidh, Farrah, Fallon, Ffion, Gina, Gia, Honor, Helen, Hattie, Hetty, Honey, Hero, Hera, Hebe, Hedda, Hazel, Heidi, Ida, Irene, Iris, Jodi, Jamie, Jordan, Jayla, Juno, Jessie, Katrin, Kayleigh, Kylie, Kelsey, Keeley, Karen, Kitty, Lila, Lara, Lana, Laura, Laurel, Lorna, Lisa, Lyra, Lyla, Lena, Luna, Leah, Lois, Leslie, Linda, Marie, Mary, Mabel, Mildred, Mina, Mila, Mala, Mara, Mindy, Missie, Marnie, Marcia, Monique, Michelle, Morgan, Nina, Nadine, Nancy, Nuala, Noelle, Nia, Nyah, Nora, Nesta, Nicole, Orla, Olga, Olive, Piper, Pepper, Peyton, Paisley, Presley, Polly, Posy, Peggy, Queenie, Rhian, Riley, Reagan, Rowan, Romy, Rivkah, Raina, Sorrell, Saffron, Sadie, Stella, Sinead, Siobhan, Susan, Sylvie, Stacy, Tina, Tracy, Tara, Tessa, Tamsin, Taylor, Toni, Tori, Una, Wanda, Wendy, Willa, Winnie, Xanthe, Yasmin, Zia, Zillah, Zelda, Zaina.