Something with a retro/vintage vibe that's not too popular (because I see Arnie as the same as Alfie and Archie but much, much less commonly used and therefore fitting with a completely different set of girls' names - not Millie and Rosie etc). How about:
Agnes, Ada, Blythe, Belinda, Clarice, Cecily, Daphne, Diana, Enid, Emmie, Freda, Fleur, Georgette, Gail, Honor, Hebe, Ida, Irene, Judy, Jocelyn, Kirsty, Kaye, Lucinda, Lillian, Maggie, Mary, Nita, Nancy, Opal, Olive, Peggy, Pearl, Queenie, Rita, Ruth, Sylvia, Sally, Tessa, Thalia, Una, Ursula, Verity, Vita, Willa, Wendy, Yvette, Yolanda, Zoe