Greer simply doesn't sound like a name at all. And if so, it should be for a boy (it's unisex though). I find
Sheridan suitable for both genders.
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Eve,
Hadia,
Keira,
Kim,
Liv,
Madison,
Neve
Only as MN:
Samantha,
Erin,
Emma,
Ebony, Ellinor,
Eileen,