Avery IS a male name but more and more girls are being given it. Name nerds tend to dislike that because when there are so many names in each gender category there is no reason to "steal" one from the other.
If you like
Freya, I'd also look into
Frida,
Greta, Joya,
Priya,
Thora,
Ylva, or
Oona.
If you like
Ava, I'd also look into
Ada,
Eva,
Una,
Ina, or
Mia.
If you like
Evelyn, I'd also look into
Emmeline,
Adeline,
Aveline (you could use your nn
Ava), or
Evelina.
"Okay, what are your ideas?
Taylor? Uh-huh.
Fletcher?
Cooper?
Tanner? Where are you getting these? The Big Book Of Medieval Professions?"