Rib cap is the traditional name in United States. Outside that tradition, butchers carry comparable beef cuts under different names — sometimes the same anatomical piece, sometimes a close cousin. The alternatives below are grouped by country so you can match what your local butcher actually carries.
On a whole prime rib roast, the rib cap is the outer ring around the eye. Increasingly butchers separate and sell it as a stand-alone premium cut.
Anatomically attached — the rib cap is the spinalis dorsi muscle that sits on top of the longissimus dorsi (the main ribeye muscle). On a bone-in roast or whole ribeye it's part of the same cut; sold separately, it's the prized outer crescent removed from the eye.