Peaberry is a term for a special type of coffee. Wikipedia, who can definitely explain it better than I ever could, describe it as:
Peaberry, also known as caracoli, is a type of coffee bean. Normally the fruit (“cherry”) of the coffee plant contains two seeds (“beans”) that develop with flattened facing sides, but sometimes only one of the two seeds is fertilized, and the single seed develops with nothing to flatten it. This oval (or pea-shaped) bean is known as peaberry. Typically around 5% of all coffee beans harvested are of this form.
The name was something that I picked up on when taking a coffee course in London at the end of 2014, and has stuck ever since. Whether this will be the name of the final business who knows, but I kind of like it and it sure beats Starbucks as a name in my opinion!