I worked at the fruit and veg market for a while in SA. One of the customers was "House of Organics"
Some of the other names that were quite clever,
Adams Apple
Banana Bowl
Banana Palm
Banana Boys
Fruit Barrow
Wild Salad
Fruitaramma
DooF DooF (we know food backwards)
Yummilicious Mum
Lettuce Inn
Veg Out
Be careful by using the word "Organic" in a name as it may limit your business as a lot of produce cant be grown organically or is quite substandard at best. (white onions are a prime example)
Just think a little further down the track, might you be JUST organic or maybe general fruit and veg.
Herbs like mint, coriander, rosemary, sage, dill, thyme, chives and bay leaves always sell well and are easy to grow, rhubarb is always a good seller.
And if you have room to plant a hedge make one from variegated and or dark green HOLLY and trim it the week before Christmas, you would be surprised what you can sell the trimmings for.
Also plant a "kaffir lime" tree the leaves sell for about 40-50c each (just think what a 3m tree is worth

) [store them in small sealable lunch bags in the freezer]