Jamie is definitely not just a male name. In fact it's arguably more female as male Jamies tend to be short for James whereas female Jamies are just Jamie. It's not popular at the moment for girls but I went to school with 3 of them in the 90s.
I think most of the shortened names and traditional names that can be unisex have been said already.
There's also nature/hippy names:
River, Storm, Phoenix, Ash, Ocean, Blue
Place names:
Paris, Rio, Dakota
American/Gaelic names:
Addison, Aubrey, Bailey, Brynn, Colby, Cameron, Cassidy, Dylan, Eden, Emerson, Erin, Fallon, Genesis, Harley, Hadley, Jordan, Kennedy, Morgan, Mackenzie, Parker, Quinn, Riley, Spencer, Sutton, Taylor
and names which sound the same but have different spellings and/or origins for different sexes:
Noah/Noa
Robin/Robyn
Billy/Billie
Jesse/Jessie
Rhys/Reese