Names I think are properly unisex are Robyn, Rowan, Ashley, Linden.
Then things like Alex, Sam/Sammy, Bobbie, Stevie, Billie, Frankie, Charley etc, but they are all diminutives of feminine versions of names. Samantha, Stephanie, Alexandra, Francesca, Wilhemena, Charlotte etc.
Choosing something like Dylan, Rory, Cameron or James isn't choosing a unixes name, it's just giving a boy's name to a girl. Not the same thing.
I could name a boy Emma or Rebecca tomorrow. That wouldn't make it unisex, it would just make people pull funny faces and feel sorry for him.