Posie/Posy - it's sweet but seems like a small child's name. I know a Posy short for Josephina but granted that's not an obvious diminutive.
Primrose - pretty. You could potentially use Posy for short.
Remi - like it. Cool and quirky.
Rue - dislike. It doesn't sound like a complete name. I only know it for a boy as short for Reuben.
Emi - Ok as a diminutive for Emma, Emily, Emmeline, Emilia etc. Doesn't seem finished on its own.
Tatum - Very American. Sounds more like a boy's name to me though I get it's probably unisex. Not keen.
River - like it but more for a boy. It's quite for a girl too though.
Bonnie - not keen. A bit twee.
Other ideas:
Amberley, Aven, Ariel, Aphra, Bronte, Blair, Cleo, Carys, Celyn, Delphi, Dulcie, Devon, Effie, Etta, Enya, Everly, Fallon, Fern, Genesis, Giselle, Hadley, Hebe, Inez, Juno, Juniper, Kendra, Kiki, Keltie, Leonie, Livia, Mika, Mala, Misty, Nova, Noa, Nyah, Odette, Piper, Pippi, Quinn, Romy, Robyn, Rowan, Ramona, Saffron, Star, Sadie, Taryn, Tegan, Tess, Vivi, Vashti, Zia, Zeryn