I like Rose! I know one whose family went down the botanical route and ended up with a Lily and a (sweet) William.
For girls, I like Laurel, Tansy, Camellia (a favourite plant, but I always struggle to grow them!), Angelica, Fern, Ffion (pronounced 'Fee-on'; it's the Welsh form of 'foxglove'), Aster, Heather, Iris/Eirys, Holly, Jasmine, Primrose, Saffron, Viola. Azalea could grow on me, and I love the shrubs! There's also Veronica, Poppy, Lavender, Rosemary, Sakura (Japanese for 'cherry blossom'), Virginia (but this could lead to teasing, unfortunately, as would Peony and probably Cherry), Myrtle (it's a bit early to bring that back, though!) and Posy. I always thought that Nicotiana would make a nice name, but unfortunately, it's the Latin name for the tobacco plant...
For boys, I was quite taken by Clematis (Clem) in a book, and know a young Heath. Indigo is a possibility, too. Unfortunately, Basil just reminds me of a dog's name! It would make me smile, though!
If we're branching out to trees, there's Acer, Aspen, Willow, Rowan, Oleander, Sequoia, Linden, Cassia, Elowen, Acacia, Ebony, Olive, Juniper...