Quite frankly, Cool Beans and Big Shots are horribly cliched and terrible names. I would be embarrassed to own a shop with either name.
Blue Rabbit isn't great (it's not horrific like the others) but you'll probably have some recognition problems with Blue Bunny Ice Cream.
Do you know the clientele you wish to attract? Perhaps a name marketed to that crowd might be best.
If someone heard your names would they know you were a coffee shop? If I think of Cool Beans it makes me think of a shop that sells trinkets and stuff. Big Shots sounds kind of snobbish and The Blue Rabbit reminds me of Rabbit food.
What about something like Blue Ridge Coffee Company or Blue Ridge Cafe. It sounds more upscale to me.
My shop is called Forbidden Flavours, anyone from out of the area would have no idea that we are a coffee and ice cream shop. Unless they saw the signs. Its a franchise so we could not pick our own name.
I hope this helps. Just be careful because partnerships are difficult. Good luck