Hmm, I've thought of a lot of "unusual" and "unique" names before... I'll list down a few of them with their matching nicknames!
Amelia - Lia, Amy, Milly
Adelaide - Addy, Lei
Desiree - Des, Desi, Rae
Delaney - Dellie, Laney
Emmeline - Emma, Lina, Emmy
Faelan - Fae, Lyn, Lenny
Genevieve - Genna, Evie
Henrietta - Etta, Ettie, Hattie
Leilani - Lei, Lani, Leila,
Lorelei- Lei, Lora, Rory
Nicolette - Nicole, Nika, Colette
Odessa - Dessa, Odie, Ada
Seraphina - Phina, Seri, Sera
Skylar - Sky, Lara
Trinity - Tia, Trin, Trinny
Yvonne - Eve, Evie, Vona, Vonnie
Zaidee - Zai, Dee, Aidy
Anyway, I hope this would be able to help you!