Lamb shank is the traditional name in United States. Outside that tradition, butchers carry comparable lamb 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.
Same primal — the shank is the lower half of the rear leg, sold separately when the leg is broken down for retail. Whole leg is for roasting; shank is for braising.
Both braise to a gelatinous, fall-apart texture; shank gives a single neat portion where neck gives shreddable meat.