Random ideas (most of these probably won't work for your setting, but I'm just brain-vomiting various Aiden-like words:)
Aedin
AedanAeden
Aerin
ErinErynEirianAidanne
Aidenne
Aeryn
Aedyn
Aidyn
AydenAodhanAodhana
Aidana
Aidena
Aedina
Aedana
Aedenna
Aelin
AylinAilenAilyn
AilinAilinn
EileenEdana (feminine form of
Edan which is a variant of
Aidan)
Keegan or
Kegan (sort of boyish but comes from the same root as
Aiden. And I know 2 female Kegans.)
Azar,
Nina, Ignatia, and Pyrrha have "fire" meanings but have nothing to do with
Aiden.
Fiera means "proud" but definitely reminds me of "fire"/"fiery"
Brynn, Brynna, Brynni, Bryni (Bryni = old english name meaning "fire" (according to definition of
Brenton)
Kenna,
Kenina, Cina? (
Cinaed means born of fire and that's what
Kenneth comes from)