Which doesn't mean it wouldn't be fitting for the exact reason EmberFox mentioned. Probably not even what you meant. But Phoenix sounds nice, so if that's a name you'd at least try... (I still use the chosen name I used for trying some out)
The list of unisex and fem names I collected for finding a name for myself:
Rain/Raine/Rayne
Cameron
Charlie
Raven
Ace
Sage/Saige
River
Onyx
Micah
Angel
Sora
Taiga
Abyssal
Lucy (Lucifer)
Link
Tundra
Solace
Paulin
Gray/Grey
Kris
Sparrow
Quinn
Gwendolyn
Sam
Morgan
Triss
Raine Lucy
Lucy Raine
Joy
Farah
Freja/Freya
Lyra
Fyra
Gwendoline
Madeline
Lizzie
Pomni
Mace
Toni
Amy
Autumn
Lzzy
Hope
Moon
Sammy
Zoe
Zoey
Olin
Error
Stella
Lara
Millie
Maddy
Emilia
Beverly
Hana
Kristen
Luna
Milena
Mila
Fiona
Brunhilda
Maple
Tiara
Anna
Yara
Jara
Aida
Emily
Clarice
Starling
Joanna
Lorraine
Buffy
Amy
Mira
Emily
Allison
Tara
Willow
April
Holly
Lena
It's the number they always claim. I know it's false, just added it for realism because it wouldn't be an "argument" otherwise.
I mean, it's obvious that the number is as wrong as a number could be, they should just honestly think about it.