I like both. Prefer Thea.
Unique is almost impossible because, unless you make one up, you've got to know the name to think of the name.
The closest I've found to a unique name (ie I taught someone with this name, have never seen it before or since and it doesn't come up on Google as a name for anyone but her) is:
Chymme (pronounced Chime like a doorbell)
But I imagine her parents must have made it up.
Other children I've taught whose names I have never come across again in real life are:
Clea, Athene, Neriah, Dami, Fabia, Delphi, Sephora and Katinka
Also knew a woman called Tree once who said it was not short for anything.
Otherwise, I think these names are very unusual:
Aven, Aspen, Allegra, Ariadne, Aphra, Atlanta, Antigone
Bernadette, Belen
Celyn, Clarice, Charity, Calypso
Danica, Devora, Dulcie
Elara, Elowen, Eilidh, Evadne, Elisaveta, Eustacia
Frederica
Giselle, Glory, Griselda
Hebe, Honor, Hero, Hera
Imelda, Indiana, Isadora, Irma
Juniper, Joelle, Jacinta
Karensa, Kiki, Keltie, Keziah
Luana, Liora, Lettice, Leticia, Lavinia, Liandra, Lux
Mala, Mika, Melisande, Morwenna, Minerva, Mirella
Nyah, Nuala, Nyla, Nerilly, Nova
Ocean, Octavia, Odette
Pandora, Posy, Persephone, Pippi
Queenie
Rivkah, Rosina, Rowena, Rhiannnyd, Rafaela, Raine
Sorrel, Saffron, Samaris, Sapphire
Thalia, Tamara, Taryn, Tansy, Tora
Una, Ursula, Ulrika
Vashti, Veda, Vanessa
Winona, Winter
Xanthippe, Xanthe, Xenia
Ysanne
Zeryn, Zillah, Zelda, Zipporah, Zia, Zola
Or, there are names which were either common or at least well known in the past but would be very unusual for your baby's generation:
Avis, Alma, Arlene, Angela, Anita, Annalise, Annette, Alison
Beverley, Bryony, Bridget, Belinda, Bertha, Beryl, Brenda, Barbara
Caroline, Carol, Claire, Celia, Cynthia, Candice, Chantelle, Charmaine
Dawn, Donna, Deborah, Denise, Darrell
Eileen, Elaine, Enid, Ethel
Freda, Fiona
Geraldine, Gloria, Gertrude
Hilda, Hilary, Helen, Heather
Irene
Jean, Joan, June, Judy, Janice, Justine, Janine, Judith, Jeanette, Jennifer, Jane, Joyce, Joy, Jacqueline, Jodie
Kathleen, Kaye
Linda, Lynne, Louise, Lynette
Mandy, Maud, Mildred, Melissa, Melanie
Nadine, Natalie, Natasha
Olga
Pamela, Paula, Pauline, Patricia
Rita, Ruth, Rosemary, Rachel
Susan, Shirley, Sheila, Sandra, Sally, Suzanne
Tiffany, Theresa, Tammy, Terri, Toni, Thelma, Thora
Virginia, Veronica, Vera
Wendy, Wanda, Winifred
Yvette, Yvonne, Yolanda