I love her coloring! It is very similar to the very first rabbit I had.
In a meet situation, the bunny is going to be a bit stressed. It's no surprise that she wasn't interested in eating.
Anything sweet (or treats) should really be avoided completely for several weeks when you get your bunny home. A new bunny in a new home will already be stressed getting adjusted to all the new sights, sounds, and smells of the new place. The last thing you want to add to a stressed rabbit is sugar. Mental stress alone can induce stress of the GI tract. Add sugar, and GI stress is even more likely.
On that note, remember that she should be left alone for her first 48 hours at your home. that means no petting, holding, or even reaching into the cage to pet her. No need to clean her litter box either in that time. The potential odor would actually be good to help her establish her litter box.
Here's more on what to do the day you bring her home.
As for breed, we'll need some better photos that show her more, also weight and age. I believe that the coloring on her back (all we can see) can be on a number of different breeds.
This is my "go to" for name ideas:
Do you have any favorite movies or books? You can use character names from those.
Or you could choose names based on a theme:
You could consider plant names like Basil, Pepper, Pumpkin, Rose, Daisy, Ivy.
Food names like Latte, Mocha, Snickers, Peanut, Burrito, Coffee, Popcorn, Cinnamon, Honey.
Or "sky" names like Orion, Pluto, Neptune, Draco, Galaxy, Nebula, Venus, Galaxy.
Or rock names like Quartz, Malachite, Copper, Clay, Diamond, Silver, Marble, Slate, Coal.
Or weather names like Blizzard, Volcano, Storm, Dusty, Sunny, Cloud, Rain, Frost
Or based on color (depending on color of course) like Ginger, Cinnamon, Onyx, Vanilla, Cream, Snow, Midnight, Shadow, Cocoa, Butter, Spot, Speckles.
