In almost any other breed of rabbit, this color is called chestnut agouti (in the U.S.) In the Rex breeds, it is referred to as castor (actually, a "good" castor is a much deeper, redder shade than your basic chestnut, and some breeders do differentiate between the two. Some judges do, too.) The name "castor" is part of the Rex breed history. I've read that some short-coated sports had been cropping up here and there for quite a while, but a breeder in France decided to breed for it, and introduced them as a separate breed in 1919. Apparently, when you cure a beaver skin, the long hairs fall out, leaving the very dense, short undercoat. The coats on these rabbits reminded the breeder of a beaver skin, so he called his new breed "Castor Rex" (Castor is the Latin name for beaver, so the name translates "King Beaver"). The original color was the basic agouti, other colors came later. The breed name has been shortened to Rex, but the Castor part lives on as a name for a color that, done well, isn't seen in any other breed.
Congrats on the new kiddos!